Measure Reference

Kinds of Windows
    Stack, List-of-attributes, List, Converted Values, Periodic Table,
    Hierarchy, Equation, HTML, About, Registration, Measure News

Menu Items
    Measure, File, Edit, Go, Info, View, Stack, Math, Units, Window, Help

Kinds of Windows

Stack window

Measure opens an empty Stack window for you automatically. Think of a Stack window as a worksheet; it's the central place to which you can bring values to work with them. (You can open multiple stack windows if you wish.)

You can add data to the stack window in a variety of ways. The most-recently-entered values show up at the bottom, and many commands operate on the most-recent one or two values, by removing the values and replacing them with a result. Results of the most recent operation are marked with vertical black bars on the left.

Double-clicking a value in a list window enters it into the stack for you, complete with a descriptive tag to remind you where the value came from. This way, you see all the intermediate results as you work with your data.

Though the Stack metaphor suggests that you enter values, one at a time, and then operate on them, you can equally well type a simple or involved expression, and just see the answer added to the stack (try 20 feet * 30 feet + 1 acre).

You can drag stack items to rearrange them. You can also drag them in and out.

Undo works immediately after any stack operation.

You can click, Shift-click, and Command-click items to select more than one at a time. Many commands operate on all the selected items. For example, Negate modifies each value in place, and Add adds together any number of items, leaving a single result.

You can do a lot of math (mostly arithmetic, some algebra) in the stack window. The units stay attached your quantities throughout, and it won't let you make mistakes (like adding "seconds" and "feet"), though you can certainly create senseless combinations of units.

Measure implicitly converts units when necessary (2 feet, 1 inch, + gives 25 inches), but it won't generally convert further than necessary. For example, it does not convert everything into base units, such as meters, kilograms, and seconds, unless you ask it to (see Collapse Units Fully in the Units menu).

A black bar to the left of an item indicates that it is a result of the most recent operation.

You can drag things from a list window to the stack window.

Here's what all those buttons at the bottom of the Stack do.

Top row:

	Add two items, or all selected items. The resulting units are those of the last item. (Shortcut: + Return)
	Subtract two items, or all selected items. That is, start with the first item and subtract all the others. The resulting units are those of the last item. Read more about subtracting dates and temperatures. (Shortcut: - Return)
	Multiply two items, or all selected items. (Shortcut: * Return)
	Divide two items, or all selected items. That is, start with the first item and divide it by all the others. (Shortcut: / Return)
	Raise an item to a power. For example: 2 feet Return 3 Return is 8 feet³. (Shortcut: ^ Return)
	Take the reciprocal of the most recent item, or all selected items. For example, 4 becomes 0.25, and 0.1 feet becomes 10 per foot. (Shortcut: \ Return)
Equations	Show a list of equations that apply to some of the items on the stack. From that list, you can double-click an equation to replace stack values with the result of applying the equation. Note: When one or more stack values are selected, lists equations that apply to the entire set of selected values. With no selection, includes equations that apply to some or all of the most recent stack values. (Tip: If you have 2 or 3 items on the stack and want to limit the equations to just the ones that apply to all the values at once, try Select All.) (Shortcut: Apple-=)
Convert	Open a window (or one window for each selected item) showing the value converted into various units.
Best	Express item(s) in the "best" available units. From among all the common units, Measure chooses the one that leaves the number closest to 1 (or -1). (Shortcut: Apple-B)
Fraction	Toggle fraction-display on or off for one item, or for all selected items. For example 0.5 becomes 1/2, but 0.12345 looks the same regardless of its fraction setting.
Swap	Swap two items, or rotate all selected items. (Shortcut: s Return)
Drop	Remove one item, or all selected items. (Shortcut: Apple-Delete or d Return)

Bottom Row:

	Square the most recent item, or all selected items. (Shortcut: Q Return)
	Take the square root of the most recent item, or all selected items. For example, the square root of 25 meters² is 5 meters, and the square root of one acre is about 208 feet. You cannot take the square root of a value if the result would have fractional dimensions. (Shortcut: q Return)
	Cube the most recent item, or all selected items.
	Take the cube root of the most recent item, or all selected items.
	Decompose the most recent item (or all selected items) into component parts. Depending on the item, this can mean several different things: a list becomes separate items; a quantity with units attached is separated into the quantity and the individual units; an expression is separated into smaller pieces; an integer becomes a list of its prime factors. (Shortcut: Apple-])
	Negate the most recent item, or all selected items. (Shortcut: n Return)
How Big?	Show a window (or one window for each selected value) putting the value into perspective compared to smaller and larger values with compatible units. (Shortcut: Apple-Shift-B)
Similar	Show a window (or one window for each selected value) listing all comparable values. For quantities, this means all the quantities in the database that have compatible units. (For database items, this means all items sharing the same is a parent; for example, with "Earth" on the stack, the Similar command opens a window listing all the planets in the database.) (Shortcut: Apple-Shift-S)
Collapse	For the most recent item, or all selected items, change the units by just one step toward the more fundamental units. This is the same as "Collapse Units Partially" in the Units menu. Repeating this operation until nothing changes is the same as "Collapse Units Fully". (Shortcut: Apple-U)
Cascade	Toggle cascade-display on or off for the most recent item, or all selected items. For example, 1.5 feet becomes 1 foot 6 inches, but 18 inches looks the same regardless of its cascade setting.
Say	Speak one item (or all selected items) out loud. (Shortcut: Apple-0)
Clear	Clear the stack, removing all items. (Shortcut: Apple-Shift-Delete)

Command line

The command line will fill in what you're about to type, whenever it's unambiguous.

Click the completion pop-up to the right of the command line to see what Measure is expecting you to type next.

To review (and re-use) your your previous commands lines, use the Up and Down arrows.

Things you can type in the command line:

Numbers in various forms, from simple to complex:
- 7
- 1.23e4 or 1.23x10^4
- 6 foot 1
- 5,000 dollars per square foot
- 2 meters per second per second
- 77±5 people per meter^3
- 77.1 — means 77.1±0.05; 77.1. means 77.1 exactly
- 2/3 minute
- 2 / 3 minute (the spaces around the "/" make this "2 divided by (3 minutes)" rather than a two-thirds of a minute)
- 8#777 — an integer in base 8. You can use any base from 2 to 36. Optional "_" separates every 4 digits for bases 2 and 16, and every 3 digits for other bases.
- 0xA987 — a base 16 integer
- 0x06ß (Option-S) -- "kabillion" notation pads a hex number to 8 digits with trailing zeroes (just like in Apple's MacsBug debugger)
- 0b10101 — a binary integer
- Constants, such as "pi"
Dates, in the following forms (the periods are optional in "A.D.", "B.C.", "B.C.E.", "A.M." and "P.M.", and lowercase letters are accepted as well):
- date 2001
- @2001
- @50 B.C.
- @700 A.D.
- @2001±5
- @31-Jan-1999
- @31-Jan-1999 11:45:59 P.M.
Expressions such as (2 + 3 miles) / height of Eiffel tower. The available operators and functions are:
- ^
- * ÷
- + -
- - (negation)
- ! (factorial)
- sqrt(n) (or Option-V)
- sin(n), cos(n), tan(n)
- asin(n) or arcsin(n), acos(n) or arccos(n), atan(n) or arctan(n)
- log(n), ln(n)
- "of", as in diameter of Earth or height of Eiffel Tower
- now
- here
Parentheses around "n" are shown above for clarity, but are not required.
Database items by name (examples: Earth, USA, California). These generally open into separate windows, but you can enter them onto the stack by using Apple-Return.
?item — open a window showing the attributes of an item (for example, planet opens a list of planets, but ?planet opens a window for the "planet" database item)
attribute relation value to open a window showing items that qualify. — Examples: in = Nevada or height < 2 feet"
{} — enters an empty list onto the stack
? or Help
=units or in units or as units to convert values to specific units
.attribute or "attribute of" to replace the most recent item, or all selected items, with the respective values of the specified attribute. — For example, Earth Apple-Return, Mars Apple-Return, Select All, diameter of Return.
Ranges of values, such as 2 to 6, 0 to 50 by 5, or 1 foot to 10 feet by 9 inches.
Commands like + 3 to add three. In general, you can enter an expression with an operator before or after it, to replace the most recent value (or all selected values) with the results of evaluating this "partial expression" once for each item, with the item filling in the "empty" spot:
- * 2 — multiplies each item by 2
- + 3 ft — adds 3 feet to each item (resulting units will be feet)
- 3 ft + — adds each item to 3 feet (result retains original units)
- - 5 — subtracts 5 from each item (if you omit the blank, -5 just enters negative five onto the stack)
- / 5 — divides each item by 5
- 5 / — divides 5 by each item
- ^ 10 — raises each item to the tenth power
- 2 ^ — raises 2 to the power of each item (Example: 0 to 10 Return, Select All, 2 ^ Return)
NOTE: Your expression gets computed just once, separately from the operation to be applied. This means, for example, that - 5 + 1 subtracts 6. It does not subtract 5 and then add 1.

(If you want to type commands by name, you can do that, too. Type "commands" to get a list.)

List-of-attributes window

Shows the details for one item.

For example, double-click on the name of a state, or type it (CA is California, while Ca or ca is Calcium). The entire window shows information about a single item. The first column lists attributes (abbreviation, population, area, etc.), and next to each attribute is its value. Double-clicking on a value enters the value into your frontmost stack, or opens a new window to display the item you clicked on. — But double-clicking in the first column, the attribute column, opens a new list-of-items window to show all items in the database that have that attribute (example: CA, double-click on "capital" to list all capitals).

Values that are automatically computed, rather than stored explicitly in the database, appear with "(*)" afterwards. Values which are inherited from a parent item are marked with a "(^)" (pointing "up" in the tree of items).

You can Apple-click the window title to see the "is a" path for the item, and to open any item in the path. Add Shift- to see the "in location" chain instead.

List window

List of Items window — for example, double-click "states" in the Table of Contents (or type "states" on the command line). Each line refers to a different state, and each column shows a particular attribute. Double-clicking on a cell enters a value into your frontmost stack window, or opens a new window to display the item you clicked on.

When there are multiple columns in a window, it makes a big difference which column you click in.

You can add columns to a List window by choosing from the View > Add Column menu.

"Comparison" columns display red bars indicating the relative sizes of the values. When some values are too large or too small to be displayed, you can double-click on such a value to re-scale the column, bringing that value into range.

Apple-click and Apple-Shift-click show the "is a" and "in location" paths, as above.

Converted-Values window

The "Convert" button (or "Show Conversions" menu item) opens a Converted-Values window, showing your value in a variety of different units. If some of the available units are obscure, only the more common ones will be shown initially; cilck the "Show All" checkbox in the window header to see the others.

Tip: There is a "#" icon in the window title, representing the original value. You can pick it up and drag it. You can also Command-click the window title to see a sequence of equivalent values, equivalent to choosing "Collapse Units Partially" repeatedly.

Periodic Table

Shows the atomic number and abbreviation of every element. You can navigate by using letter keys (type the first letters of an element's name or chemical symbol), arrow keys, or number keys.

Click any element to see its full name and element category. Double-click to open an element.

"Open List" opens a list window showing all the elements.

You can also pick up an item and drag it.

Hierarchy window

Use the arrow keys, letter keys, Tab, and Shift-Tab to navigate. Double-click to open an item, or Apple-I for Get Info.

You can also pick up an item and drag it.

Equation window

Displays an equation, and a table of all the equation's variables. If you fill in values for all the variables but one, Measure automatically solves the equation for the remaining variable and fills in the answer.

You can drag the answer to the Stack window (or use Copy and Paste). Even without moving it to the stack, you can display the result in different ways by choosing Best Units from the Units menu, or by choosing Cascade and Fraction options from the View menu.

Without entering values, you can solve the equation for any variable by selecting the variable and clicking the "Isolate" button.

Clear All removes all variable values and restores the equation to its original form.

Clear removes only the selected variable values.

You can pick up and drag the equation, or any subexpression of it (click on the "=" to get the whole equation; click on any operator to get the piece that includes that operator and its operands). If you just click and don't drag, the expression is added to your stack window.

HTML Window

These include Help, Tutorial, Examples, Reference. Underlined blue text represents a link you can click to follow.

About box

Shows the version number and registration status of Measure. There is also a Register button you can click to bring up the Registration window.

Registration window

Enter your name and registration code here, and Measure will stop reminding you to pay. You'll even get to hear Sarah say "Thank you."

Measure News

Shows up when you choose Check Web For Measure Updates from the Help menu, or when you accept Measure's occasional offer to check for you.

All Menu Items

Measure, File, Edit, Go, Info, View, Stack, Math, Units, Window, Help.

Measure menu

About Measure	Displays the About box, which describes your license status and includes a `Register...` button.
Quit Measure	Quits.

File menu

Close Window	Closes the frontmost window.
Close All	Closes all Measure windows. (Many operations, including typing, will create a new Stack window if none is open.)

There is no Save or Save As, because Measure does not save any documents to disk. However, you can Copy your results and Paste them elsewhere.

Edit menu

Undo Redo	You can undo or redo the most recent operation on the frontmost stack window, or your most recent typing into a stack window.
Cut	Removes text from an edit field, placing it onto the clipboard. (Use Show Clipboard in the Finder to see what's on the clipboard.)
Copy	Copies text from an edit field, or from one or more selected items, onto the clipboard.
Paste	Pastes text from the clipboard into an edit field.
Delete	Clears the selected text from an edit field, or blanks out a variable value in an Equation window.
Select All	Selects all the text in an edit field, or all the items in a column.
Select None	Unselects selected text in an edit field, or unselects all items in the frontmost window.

Go menu

Table of Contents	Opens (or brings forward) the "Contents" window (which is automatically opened when Measure starts up).
Kinds of Units	Opens (or brings forward) the "Kinds of Units" window, including over 60 different categories such as length, area, volume, speed, temperature, money, and rate of pay. (Explore by double-clicking, and also by selecting and using Get Info.)
All Units	Opens (or brings forward) the "All Units" window, listing every measurement unit in the database.
Everything	Opens (or brings forward) the "Everything" window, listing almost everything in the database. (To include items normally hidden, hold down Option while choosing the Everything command. The items are hidden because they relate to Measure's internal operation.)
Hierarchies >	Choosing the Hierarchies menu item itself opens (or brings forward) the "Hierarchies" window, listing every attribute that defines a hierarchy in the database. You can double-click an item in that window, or just choose the one you want from the sub-menu. The more interesting (deeper) hierarchies are listed in boldface.
Periodic Table	Opens (or brings forward) the "Periodic Table" window, showing a table of all the elements. Click an element to select it and identify it. Double-click to open an element in its own window. You can also drag an element.
Examples	Opens (or brings forward) the "Examples" window (also available in the Help menu).

Info menu

Open Items	Opens the selected item(s) (or the most recent item on the stack). Exactly what happens depends on the type of the item. For example, opening "building" displays a list of buildings. Opening a numeric value just adds it to the stack.
Get Info	Opens an "List of Attributes" window for the selected item(s) (or for the most recent item on the stack). For numeric values, you'll get a window describing each component of the units. For example, Get Info on `5 feet/second²` opens a window for Foot and another for Second.
Conversions	Open a window (or one window for each selected item) showing the value converted into various units.
How Big Is This?	Show a window (or one window for each selected value) putting the value into perspective compared to smaller and larger values with compatible units.
Similar Items	Show a window (or one window for each selected value) listing all comparable values. For quantities, this means all the quantities in the database that have compatible units. (For database items, this means all items sharing the same "is a" parent; for example, with "Earth" on the stack, the Similar command opens a window listing all the planets in the database.)
Speak	Pronounces the selected item(s) out loud.
Stop Speech	Interrupts speech.

View menu

Add Column >	Allows you to add another column to a List window. The submenu lists all the attributes that apply to one or more items in the list. (Columns already present in the window are not listed.)
Remove Column	Removes a column from the front List window. (If you have a single item selected, the menu item offers to remove the column containing it. Otherwise, it offers to remove the current sort column.) You can't remove the "name" column.
Convert Column to (units)	When you have one value selected, offers to convert all the values in that column to have the same units as the selected value. — This will not affect how the values sort or the lengths of their comparison bars, because you are only expressing the same values in different units, not changing the value.
Convert Column to Other Units...	Prompts you to enter units in which you want to express the values in the current column (the column containing your selection, or the current sort column). As above, this doesn't change the values themselves, it merely expresses them in different units.
Display As >	Binary, Octal, Decimal, Hexadecimal. Asks the selected integer values (or the most recent item on the stack) to display themselves in one of these number bases. Any value that isn't an integer continues to display itself in decimal.
Fraction Display On Fraction Display Off	Turn fraction-display on or off for the selected item(s). For example 0.5 becomes 1/2, but 0.12345 looks the same regardless of its fraction setting.
Unit Cascade On Unit Cascade Off	Turn cascade-display on or off for the selected item(s). For example, 1.5 feet becomes 1 foot 6 inches, but 18 inches looks the same regardless of its cascade setting.
Show All Uncertainties Show Large Uncertainties Hide Uncertainties	For all windows, controls whether the uncertainties are displayed (for example, `10±2 feet`). A large uncertainty is anything over 10% of the value.
Abbreviations On Abbreviations Off	For all windows, controls whether or not numbers with units abbreviate their units. (Any unit that doesn't have an abbreviation is unaffected.) For example: `5 dollars/pound` or `5 $/lb`.

Stack menu

New Stack	Opens a new (empty) stack window.
Bring Stack to Front	Brings a stack window to the front.
Duplicate Stack	Makes a copy of the frontmost stack window, complete with all the items it contains.
Clear Stack	Removes all the items from the stack.
Duplicate Items	Adds a copy of each selected item to the stack. (Shortcut: Return)
Drop	Removes the most recent item (or all selected items) from the stack. (Shortcut: Apple-Delete or d Return)
Swap	Swap two items, or rotate all selected items. (Shortcut: s Return)
Pick	Moves all of the selected stack items to the shallow end of the stack.
Now	Adds the current date/time to the stack.
Applicable Equations	Show a list of equations that apply to some of the items on the stack. From that list, you can double-click an equation to replace stack values with the result of applying the equation. Note: When one or more stack values are selected, lists equations that apply to the entire set of selected values. With no selection, includes equations that apply to some or all of the most recent stack values. (Tip: If you have 2 or 3 items on the stack and want to limit the equations to just the ones that apply to all the values at once, try Select All.)
Apply Equation	When an equation is selected in a list, or when an equation window is in front, applies the equation to the items on your stack, replacing the needed number of items with the result.
Make Exact	Sets the uncertainty of one item (or all selected items) to zero.
Set Uncertainty	Requires two items. Sets the uncertainty of the deeper item to the specified value, which can be unit-less, or can have any units compatible with the deeper value. For example: `10 feet` Return, `20 inches` Return, `Set Uncertainty` results in `10 (±1.667) feet`.
Get Uncertainty	Adds the uncertainty of one item (or each selected item) to the stack.
Upper & Lower Bounds	Splits each item into two values. For example, `10 (±2) feet` becomes `lower bound: 8 feet` and `upper bound: 12`.
Evaluate	Tries to turn a value into a number. This command is rarely useful in Measure 1.0, but here's an example where it actually does something: `128` Return, `Factor`, `Decompose` leaves you with 2⁷. `Evaluate` turns it back into 128.

Math menu

The items in the Math menu apply to the frontmost Stack window.

Add	Add two items, or all selected items. The resulting units are those of the last item. For example 6 inches + 1 foot is 1.5 feet, whereas 1 foot + 6 inches is 18 inches. You can't add two dates or two temperatures, but you can add a time interval to a date, and you can add a temperature interval to a temperature. (Shortcut: + Return)
Subtract	Subtract two items, or all selected items. That is, start with the first item and subtract all the others. The resulting units are those of the last item. You can subtract two dates to get a time interval. You can subtract two temperatures to get a temperature interval. You can subtract two map locations to get a distance & an initial bearing for a great-circle path. The result is a list of two items, which you can break apart using Decompose. (Shortcut: - Return)
Multiply	Multiply two items, or all selected items. (Shortcut: * Return)
Divide	Divide two items, or all selected items. That is, start with the first item and divide it by all the others. (Shortcut: / Return)
Power	Raise an item to a power. For example: `2 feet` Return, `3` Return, `Power` is `8 feet³`. (Shortcut: ^ Return)
Modulo	Computes the remainder when one item is divided by another. For example: `3 feet` Return, `10 inches` Return results in `6 inches`. (Shortcut: % Return)
Reciprocal (1/x)	Take the reciprocal of the most recent item, or all selected items. For example, `4` becomes `0.25`, and `0.1 feet` becomes `10 per foot`. (Shortcut: \ Return)
Negate	Negate the most recent item, or all selected items. (Shortcut: n Return)
Absolute Value	Take the absolute value of the most recent item, or all selected items.
Factorial	Compute the factorial of the most recent item, or all selected items. The items must be whole numbers. (Shortcut: ! Return)
Trig >	Sine, Cosine, Tangent. The values must be angles. (You can't take the Sine of 1, but you can take the Sine of 1 degree or 1 radian or 0.1 revolutions.) Arc-sine, Arc-cosine, Arc-tangent. The values must be dimensionless numbers; the results are angles.
Log >	Log Base e, Log Base 10, e^x, 10^x. Compute the logarithm or expontential for the most recent item, or all selected items. The values must be dimensionless. (Shortcut: l (lowercase L) Return for Log Base e.) (Shortcut: L Return for Log Base 10.)
Square	Square the most recent item, or all selected items. (Shortcut: Q Return)
Square Root	Take the square root of the most recent item, or all selected items. For example, the square root of 25 meters² is 5 meters, and the square root of one acre is about 208 feet. You cannot take the square root of a value if the result would have fractional dimensions. (Shortcut: q Return)
Cube	Cube the most recent item, or all selected items.
Cube Root	Take the cube root of the most recent item, or all selected items.
Greatest Common Factor	Computes the greatest common factor of two integers. For example, the GCF of 18 and 24 is 6.
Least Common Multiple	Computes the least common multiple of two integers. For example, the LCM of 4 and 6 is 12.
Permutations	Computes the number of permutations of X things taken Y at a time. For example, 5 Return 3 Return `Permutations` results in 60 (5x4x3). See also Combinations.
Combinations	Computes the number of combinations of X things taken Y at a time; this is different from Permutations in that the order of the things "taken" is not considered important. For example, 5 Return 3 Return `Combinations` results in 10 (5x4x3 divided by 3x2x1).
Decompose	Decompose the most recent item (or all selected items) into component parts. Depending on the item, this can mean several different things: a list becomes separate items; a quantity with units attached is separated into the quantity and the individual units; an expression is separated into smaller pieces; an integer becomes a list of its prime factors. (Shortcut: Apple-])
Factor	Replaces the most recent stack item (or each selected item) with a list of terms representing its prime factors. For example, 150 becomes { 2, 3, 5² }.

Units menu

These commands work in many kinds of windows, not just the stack. They operate on the selected items, or the most recent item in a stack. Several commands leave the value unchanged, but expressed in different units (24 inches is just another way to say 2 feet).

Best Units	Display the selected values in more fitting units. For example, 24 inches becomes 2 feet.
Convert To Other Units...	Prompts you to enter units in which you want to express the selected values.
Collapse Units Fully	Display the selected values in fundamental units. (For example, 1/2 hour becomes 1,800 seconds.) The choice of "fundamental" units is arbitrary, and includes meters, kilograms, seconds, radians, coulombs, people, bytes, dollars, and kelvin.
Collapse Units Partially	Display the selected values in units that are one step closer to fundamental units. (For example, 1/2 hour becomes 30 minutes.) Repeating this command until nothing changes is equivalent to Collapse Units Fully.
Strip Units	Removes the units from the selected values. For example, 32±10 feet/second becomes just 32±10, and 5 feet 6 inches becomes 5.5.

Window menu

This is a standard Carbon window menu. Choose a window to bring it to the front. A check mark indicates the front window. Hold down the Option key for additional choices.

Help menu

Measure Help Show Release Notes Tutorial Examples Reference	Opens (or brings forward, if already open) the corresponding window.
Go to www.UnitSoftware.com/Measure	Asks your web browser to go to <http://www.UnitSoftware.com/Measure/>.
Email measure@UnitSoftware.com	Asks your email program to address a new message to measure@UnitSoftware.com.
Check Web for Measure News	Checks with www.UnitSoftware.com and then opens a window with up-to-date Measure news based on the version of Measure you are running (for example, whether a new version is available for download).

Measure home