Help

Some quick tips to get you started:

• Input boxes can be left empty when not relevant.
• A value like five and a half feet can be entered as 5.5 feet or as 5 feet 6 inches.
• A value like six and a quarter inches can be entered as 6.25 inches or as 6 inches and 1/4.
• You can type a fairly general expression into the text box. Click the ? button for more information.

Expressions

Expressions can contain numbers, units and the operators + - * / and ^ (exponentiation). Multiplication and division are performed before addition and subtraction, and parenthesis can be used for grouping. Spaces are generally optional.

Units include: ft ' in " m and cm.

As you type, the expression might be momentarily unparsable, e.g., “3'+”, until you finish typing. The results box will be grayed out while that happens. It would be too noisy to alert each of these errors, but if you don't know why it's grayed out, you can hit “enter” to see an error message.

If you realize you should have begun a parenthesized expression and enter 10'4" + 4'2"), the opening parenthesis will be provided automatically so that you don't have to go back and add it yourself (which is annoying on mobile devices).

In these help boxes most sample expressions, like 11'4"/2, can be clicked to evaluate the expression.

Example	Description
5' 6"	An ordinary distance
5' 6 3/8" / 3	Divide 5 feet 6 and 3/8 inches by 3
5 1/2' - 8"	Subtracts lengths
5.5'	You can use decimal values instead of fractions
3/4"	You can use just a fraction
(5'6" + 7') / 2	The average of 5'6" and 7'
5' 10 3/8" * 3/4	3/4 of 5' 10 3/8"
12' / 6"	The ratio of 12' and 6"
1 + 2 * 3	Ordinary math (note order of operations; result is 7)
(1 + 2) * 3	Result is 9
1m - 2cm	One meter minus two centimeters
ft	A foot
ft * 8	8 feet; notice that named units are simply variables that have units
5' 6" * pi	Circumference of a 5' 6" diameter circle
hyp(3', 4')	Hypotenuse of a right triangle with sides 3' and 4' (result is 5')
1/4 mi2 / acres	The number of acres in a quarter of a square mile

Try furlongs/fortnight or gallons/cup.

Units

Units are either the notations ' and " for feet and inches or a named unit. The full list of predefined units and constants is too long to show here.

Any variable you define can be used as a unit itself. For example, if you enter cubit = 1 1/2', you can then use expressions like 3 cubit 5 1/2".

A unit can be immediately followed (without spaces) by a number which is the power of that unit. For instance, 3 yd2 is three square yards (27 square feet) and 2 ft3 is two cubic feet. If a unit specifier is immediately preceded by a / (without spaces), it's an inverse unit. For instance, 60 /ft2 means 60 per square foot. 144 /ft2 means 144 per square foot or, equivalently, 1 per square inch (which is how it will display). What per square foot? Anything. Think “ducks” or “pebbles” and you'll be on the right track.

In fact, you can type 640 'ducks' / mi2 or 144 'pebble'/ft2. (Bear in mind that 'pebble' is a different unit from 'pebbles'.) Try 2 'shoes'/person * 1000 people. If there's some unit this tool didn't anticipate, you can define it yourself, bogosity = 'bogosity' and use it as an ordinary unit such as 20 bogosity.

Beware that spaces can occasionally make a big difference. 1/2 in or 1/2in means half an inch, but 1 / 2 in or even 1/ 2 in means one over 2 inches. Just avoid putting spaces around the slash in a fractional unit and you'll be fine.

Unit Conversions

To display results in terms of specific units, follow an expression by : then a unit or series of units. For instance, 100 km/hr : mi displays the speed in miles/minute. 100 km/hr : mi/hr displays the speed in terms of miles/hour.

The special units mks, cgs and uscu request results in the those systems, e.g. 60 mi/hr : mks.

• How many watts in 10 horsepower? 10 horsepower : W, alternatively 10 horsepower : mks
• How many tablespoons in a cup? cup : tbsp
• How many cups in a tablespoon? tbsp : cup
• Sea-level air pressure in PSI? atm : PSI
• What's 20 degrees celsius in fahrenheit? 20 celsius : fahrenheit
• What about absolute zero? 0K : degf
• What is 20000 leagues anyway? 20000 league : mi. That's deep!
• What's pi/4 radians in degrees? pi/4 radians : degrees
• How much does it cost to run a 100 watt lightbulb for a year, assuming electricity costs $0.20 per kilowatt hour (ecost = 0.20$ / kWh)? That would be, ecost * 100 watts : year, about $175. Use LEDs!
• How much does it cost to run a typical refrigerator per month? ecost * 65W : month
• How much does it cost to watch a modern flat-screen TV per hour? ecost * 450 watt : hr
• How about a year on standby? ecost * .5 watt : yr
• An electric kettle per minute? ecost * 3000 watt : min, just one cent.
• What's 45 mpg as km/liter? 45 mi/gallon : km/liter
• How many meals do you eat in a year if you eat 3 meals per day? 3 'meals'/day : yr
• How much does a gallon of water weigh in pounds? kg/liter*gallon : lb
• What's a kilobyte per meter in kilometers? kB/m : km. It seems rather silly, but it might be a length of magnetic tape
• Remember old modems? 9600 baud * 1 bit/symbol
• How far away is the Sun in miles? au : mi
• How long does it take sunlight to reach the Earth? au/c : min
• What's a femtolightyear in yards? femtolightyear : yards
• What's the current with 5V across a 2000 ohm resister? 5V / 2000 ohm
• What's 33 1/3 RPM as degrees per second? 33 1/3 RPM : degrees/second
• Suppose an Icelandic króna is about ISK = .008$ and gas costs 220 ISK/liter; what's that in dollars per gallon? 220 ISK/liter : $/gallon
• While we're at it, what's a dollar in króna? $ : ISK

As an exercise, suppose an elephant weighs elephantWeight = 8000lbf (I've used pounds of force) and an elephant's foot is about elephantFoot = 45cm across, and it's standing evenly on four legs, then the pressure under its feet, expressed in pounds per square inch, is elephantWeight/(pi*(elephantFoot/2)^2)/4 : PSI, about 8 PSI.

Variables

To define variables type name = expression then hit “enter.” For instance, frontage = 45'4 3/4". You can then use those values in later expressions, e.g. frontage/3. And because frontage is a length, it can also be used as a unit: 1/3 frontage or 1/3frontage.

The variables ft, in, m, cm, etc. described in "Units" above are predefined for use as values or as units. The variable pi is predefined in case you care about circles. Reserved predefined variables cannot be changed.

Functions

Define functions to automate routine calculations by typing name(param,param,…) = expression then hitting “enter.” For instance, you can define a function to average to numbers or lengths: average(x,y) = (x+y)/2 (but the predefined function mean(…) already does that, so…).

Functions can refer to their parameters and to variables. As a special case, a function with no parameters can be used as a “dynamic variable.” That is, assuming variables a and b are defined (say, a = 2 and b = 3), the function ab() = a + b can be invoked as ab() or ab, and in either case gives you the current value of a + b. If you change either variable (say, b = 5), then the value ab changes too.

Built-In Functions

Function	Description
mean(x,y,…)	The average of a set of numbers or dimensional values
sum(x,y,…)	The average of a set of numbers or dimensional values
hyp(x,y,…)	The hypotenuse of a triangle or, more usefully, the diagonal of a rectangle
sqrt(x)	Square root
cbrt(x)	Cube root
sin(angle)	Sine of an angle (must be units of radians or degrees or a plain number)
cos(angle)	Cosine of an angle (must be units of radians or degrees or a plain number)
atan2(y, x)	Returns the angle corresponding to the slope y/x, even when x is zero. More formally, it's the angle from the x-axis of the vector (x,y).

For the purposes of this tool, angles are neither degrees nor radians. They are just angles and can be specified or displayed using either notation. If a plain number is given, it will be interpreted as radians. So sin(45 degrees), sin(pi/4radian) and sin(pi/4) all mean the same thing.

Metric Feet

Results presented in feet and inches show an alternate interpretation assuming measurements are in "metric feet." A “metric foot” is a convention used by the construction industry in metric countries where a foot is taken to be exactly 30cm instead of 30.48cm. It's an international standard.

Odds & Ends

Boring details, if you're interested.

Boring Details

This program started out as a quick and dirty tool to easily divide lengths given in feet and inches into equal parts, a common task in the construction industry and quite tedious to work out by hand. If the file name or URL contains the string "inch", you'll see the original user interface. If you're curious, you can switch the UI.

But I started to think of it as a calculator and wondered if it could be generalized to do arbitrary math with lengths. It's possible to add two lengths, resulting in another length, or to multiply or divide a length by a number. But you can't add a length and a number. You can divide a length by a length to get a number (the ratio of lengths). Can you multiply two lengths? Yes, but the result is an area.

This line of thinking leads to dimensional analysis, and there are already some very good programs out there for that including the legendary Unix "units" command. Hell, Google will do it for you if you ask it nicely. But I couldn't help myself, so I got carried away and ended up implementing a fairly general dimensional units calculator.

Various interesting problems came up along the way, including issues of special-purpose language design, grammar ambiguity, and maintaining full decimal precision in calculations (remember that 0.1 can't be represented exactly in binary floating point).

As an example of using ambiguity for profit, there seemed to be no principled reason to forbid using a dimensionless number as a unit and allowing it lets you define the function circleArea(r) = 𝜋 r2 or write 17 mol.

Still, the main distinction of this tool is that it deals naturally with notations typically used with feet and inches. But, sigh, Google will do that for you too.

Contra the NIST, and in accordance with conventional usage, this program treats acres, chains, furlongs, townships, etc. as if they were defined in terms of modern feet. But in fact they're defined in terms of the anachronistic "survey foot" and there's a suite of survey units with their, arguably proper, definitions: surveyacre, surveychain, surveyrod, etc. In practice, usage varies by state and is currently undergoing changes. It's a mess.

Traditional volume units are problematic. There are differences between wet and dry gallons and futhermore differences between US and UK units. "Barrels" depend on what's in them. Fruits and vegetables are pretty simple, unless it's cranberries. Altogether, the situation is rather hopeless and by default I've chosen relatively uncontroverial wet US volume units and excluded dry units entirely.

The SI system treats angles as dimensionless quantities, perhaps because they don't actually measure anything. But treating them as if they were units allows dealing with things like revolutions / minute , converting degrees to radians, and, to be fair, makes some sense when thinking about things like the reduced Planck constant (ℏ). Even the SI is torn because units of luminosity (lux and lumen) use the steradian. So, for practical reasons more than principled ones, this tool treats angles as if they were dimensional. Splitting the differences among the different angular units systems, I use the circle, a full revolution, as the basis unit for angles.

This program is unapologetically biased toward US conventional units since it was originally conceived as a tool to deal with their difficulty; nobody else has problems with units calculations. Still, I've tried to encompass the entire SI system and as much of the CGS system as possible. Unfortunately, CGS has multiple extensions for electromagnetism, all different from each other and from SI. Worse still, certain CGS electromagnetic units use half-integer dimension exponents and that's a thornier kind of dimensional analysis than this program can handle.

You can download this app locally as UnitsCalc or FeetInchCalc.

You can also run this app from the web.

A-B-C. A-Always. B-Be. C-Coding.

Copyright © 2021, Stan Switzer

Icon made by Freepik from www.flaticon.com.

The SI Units Logo, from the BIPM, is CC BY-ND 4.0.

Built-In Constants and Units

Symbols that are reserved (that is, cannot be redefined) are noted.

Symbol	Description