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Rink is a unit conversion and calculation tool which can be used for both small and simple arithmetic and more complex dimensionality analysis and other tasks. In this manual, each section will have examples of the discussed material at the top.
Table of Contents
- Working with units
- Units and prefixes
- Top-level statements
- Index of Units
Working with units
In order to understand Rink, an understanding of units themselves is required. Fundamentally, a unit is a way of assigning a concrete value to a specific quantity such as length, volume, energy, power, current, etc. Each quantity can be reduced into other quantities (for example, area is length x length), except for 7 base units.
The 7 base units (as well as their SI units):
- Length (meters)
- Time (seconds)
- Mass (kilograms)
- Current (amperes)
- Temperature (kelvin)
- Amount of Substance (mol)
- Human-subjective brightness of light (candela)
In addition, Rink defines a few non-SI base units:
- Money (Euro)
- Information (bit)
- Musical note length (wholenote)
Each of these quantities is treated as irreducible. The 7 base units are the foundations of SI, and customary systems as well. (Customary systems are defined in terms of SI.)
Every unit is composed of two parts: A numerical value, and its dimensionality. The dimensionality is how a unit relates itself to the base units. Each base unit is raised to a certain power to construct the dimensionality. For example, the dimensionality of the quantity of acceleration is length^1 * time^-2 and then the rest of the base units are to the 0th power, which is to say that they do not matter. Two units are considered conformable if they have matching dimensionalities, and they can then be used in conversions.
Because each unit has a numerical part, it is possible to do normal math on them.
- Adding two units produces a new unit with matching dimensionality.
- Multiplying two units produces a new unit with its dimensionality as each base unit multiplied together, e.g. velocity (length time^-1) * hertz (time^-1) = acceleration (length time^-2).
- Dividing two units is like multiplication, but taking away from the base units. A unit divided by itself is dimensionless, it has no quantity. Normal numbers are dimensionless.
Because of this, units are essentially just numbers. As such, Rink is essentially a calculator which takes dimensionality into account.
Weight vs Mass
It is important to remember the differences between mass and weight when working with mass and force units. Here are some tips:
Mass doesn't change depending on the amount of gravity, and directly influences momentum.
Weight is the amount of downward force on an object due to gravity.
Mass is measured in kilograms or pounds.
Weight is measured in newtons, kilogram force (kgf), or pound force (lbf).
When someone says something weighs some amount of kg or lb, they're saying it has a weight of that number of kgf or lbf. This includes things like weight on the moon. (Don't correct anyone using this common figure of speech.)
A scale displays an estimate of mass by measuring the force applied to it divided by its calibrated measurement of the acceleration of gravity. Its mass estimate would be incorrect on other planets unless it was recalibrated. You can also think of the displayed value as being weight in kgf or lbf.
You can compute weight by multiplying mass by gravity. Both kgf and lbf have earth gravity as part of their definition, so when you multiply kg or lb by gravity you get the same numerical values back, but with kgf or lbf units.
> 10.1e2 1010 (dimensionless) > 10 10 (dimensionless) > 0x10 16 (dimensionless) > 0o10 8 (dimensionless) > 0b10 2 (dimensionless)
Decimal numbers can be written with an integer component, an
after-decimal-point component, and an exponent. Numbers can optionally
U+2009 THIN SPACE or an underscore (
_) for digit place
The decimal point is always written with a dot (
.), not a comma or
other marker. If the decimal point is provided, it must be followed by
more digits. (
1. is not allowed.)
The exponent starts with an
e, followed by an integer with an
optional sign. The exponent is shorthand for writing out
* 10^exp. There can be no spaces within the number other than allowed
digit separators. (
10 e10 is not allowed.)
Hexadecimal, octal, and binary integers can be written using
0b prefixes, respectively. These literals do not currently
support decimal points or exponents.
> 3 4 m 5 s 60 m s > 3 * 4 m 5 s 60 m s
Multiplication can be either by juxtaposition (that is, without any symbol) or using an explicit * operator.
> 10 km / 5 m 2000 (dimensionless) > 1|2 m 0.5 m (length)
There are two division operators, for separate purposes.
/ has lower
precedence than multiplication, and is used mainly for separating two
halves of an entire expression.
| has higher precedence than
multiplication, and is used mainly for fractions of integers.
> 1 * 2 + 1 * 2 4 (dimensionless) > 12 meters + 5 feet 13.524 m (length)
These have lower precedence than multiplication and division.
> 12 °C 285.15 K (temperature)
Temperature scales are operators with higher precedence than addition, and lower than multiplication. See the section on temperature conversions for more detailed syntax.
> 9999999999999 approx. 9.99999e12 (dimensionless) > 1.001 1.001 (dimensionless) > 1e100 1.0e100 (dimensionless)
Numbers can be written with a fraction, and can be written in
1e24 is short for
1 * 10^24.
> 12 ft^2 435483/390625, approx. 1.114836 m^2 (area)
Powers have higher precedence than multiplication. Both
can be used.
Inline unit definitions
> ton -> rock = 10kg 45359237/500000, approx. 90.71847 rock (mass)
An equals expression is one which simultaneously defines a new unit with the right-hand side, names it using the left-hand side, and then produces it as its result. This is useful for customizing the output of the right-hand side of a conversion or converting into things that don't currently have units such as the amount of calories in a potato.
Custom base units
> 12 'core' hour / 3 'core' -> minutes 240 minutes (time)
A unit name which is wrapped in quotation marks will not be checked for whether it exists when it is evaluated. This means you can wrap anything in quotes to in effect produce a new base unit for the purposes of a single calculation. This can be useful for doing calculations in terms of things which are otherwise dimensionless.
Units and prefixes
Units can be prefixed with SI prefixes as well as a number of non-SI prefixes, such as: quarter, double, kibi, mebi, ⅞.
Rink will accept plural units.
> meter -> feet 3.280839 foot (length) > 12 °C -> °F 53.6 °F (temperature)
The left hand side of the conversion is an arbitrary expression, and the right hand side is one of:
- An arbitrary expression
- A temperature scale (celsius, fahrenheit, and several historical scales)
- A unit list (e.g. hour;min;sec)
> 2^17 seconds -> hour;min;sec 36 hour, 24 minute, 32 s (time) > 2 km -> mi;ft 1 mile, 1281.679 foot (length) > liter -> cup;tbsp;tsp 4 uscup, 3 ustablespoon, 1.884136 usteaspoon (volume)
A unit list is a comma- or semicolon- delimited list of units with the same dimensionality, which can be used for breaking down numbers into more familiar quantities.
> 12 °C 285.15 K (temperature) > 12 degC 285.15 K (temperature) > 12 celsius 285.15 K (temperature)
Temperature scales in Rink are handled a little specially, because only Kelvin and Rankine (the absolute zero version of Fahrenheit) start at absolute zero. As such, they are operators, not units. These operators have looser binding precedence than multiplication, but tighter than addition.
Available temperature scales:
℃: Celsius, the standard scale in most countries.
℉: Fahrenheit, the scale used in households across the United States.
reaumur: Réaumur: A historical scale once used throughout Europe.
romer: Romer: Yet another historical scale.
degnewton: Newton: A historical scale created by Isaac Newton.
delisle: Delisle: A historical scale which, alongside the original Celsius scale, is reversed from the scales we are used to today. Its zero point is boiling water, and the freezing point of water is 150°De.
Note that these temperature scale measurements are absolute measurements, not differences. If you wish to say something like "a difference of 1°C", then you must use the absolute scale for the scale you're using. These are:
- For Celsius, kelvin
- For Fahrenheit, Rankine
- For Réaumur,
reaumur_absolute(absolute as in the zero point is absolute zero)
- For Rømer,
- For Newton,
- For Delisle,
> 1000 -> hex 3e8 (dimensionless) > 10000 -> base 36 7ps (dimensionless) > pi meter -> hex meter approx. 3.243f6a meter (length)
Base modifiers are specified with
base followed by a number,
followed by the rest of your conversion. Allowed bases are currently 2
through 36. There are some special base names which are also
base16for base 16.
base8for base 8.
base2for base 2.
> 2^128 -> digits 340282366920938463463374607431768211456 (dimensionless) > 1/7 -> digits 50 1/7, approx. 0.1428571428571428571428571428571428571428571428571428 (dimensionless) > googol -> digits 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (dimensionless)
Digits modifiers are specified with
digits optionally followed by a
number, before the base modifier and before the rest of the
conversion. Any number of digits are allowed, but large amounts may
The function of this modifier is that it forces the entire integer part to be printed (i.e., scientific notation will not be used), and then it prints an additional n digits, using the default if not specified.
Trancendental numbers currently cannot be precisely represented, so asking for many digits of pi or e will produce unsatisfying results.
Trigonometric and logarithmic functions are currently implemented using a machine-float fallback, because their results cannot be precisely represented as finite rationals. Because of this, asking for many digits of such numbers will also produce unsatisfying results.
> units for power Units for kg m^2 / s^3 (power): VA, airwatt, boilerhorsepower, brhorsepower, donkeypower, electrichorsepower, horsepower, lusec, mbh, metrichorsepower, poncelet, sccm, sccs, scfh, scfm, slph, slpm, solarluminosity, tonrefrigeration, waterhorsepower, watt
units of, and
units commands will find more units
which match the dimensionality of the one specified.
> factorize velocity Factorizations: velocity; frequency length; area viscosity; acceleration time; length^2 viscosity > factorize power Factorizations: power; force velocity; radiant_intensity solid_angle; area radiosity; length spectral_flux_wavelength; radiation_dose spectral_exposure_frequency; spectral_irradiance_wavelength volume; temperature thermal_conductance; energy frequency; current^2 resistance; ...
Unit factorization is what Rink names the process of finding quantities which can be multiplied together to produce the original quantity. This can be useful for discovering new ways to construct a unit.
> search milk Search results: milk (density), mil (length), mile (length), mill (dimensionless), mi (length)
Allows you to search for units based on their names, returning up to 5 results and showing the associated physical quantity of the unit.
> #jan 01, 1970# 1970-01-01 00:00:00 +00:00 (46 years ago) > now - #jan 01, 1970# -> gigaseconds 1.472083 gigaseconds (time) > #2016-08-24# + 500 weeks 2026-03-25 00:00:00 +00:00 (in 9 years)
In addition to handling units, Rink is also capable of doing some calculations with dates and times.
> milk milk: density = 242 gram -> approx. 236588.2 millimeter^3 > gallon milk milk: volume = approx. 3785411.7 millimeter^3; mass = 3.872 kilogram > egg egg: USA large egg. mass_shelled = 50 gram; mass_white = 30 gram; mass_yolk = 18.6 gram; volume = approx. 46824.75 millimeter^3; volume_white = approx. 29573.52 millimeter^3; volume_yolk = approx. 17251.22 millimeter^3 > egg_shelled of kg egg 20 (dimensionless) > gallon gasoline -> btu gasoline: volume = approx. 3785411.7 millimeter^3; energy_HHV = 125000 btu; energy_LHV = 115000 btu
Substances are how Rink organizes the physical properties of materials, objects, both countable and uncountable. Each substance has a name, an associated amount (defaulting to dimensionless 1), and a set of associated properties.
Each property maps a named input into a named output and vice versa, and has a name itself. Countable objects often have properties with an input being dimensionless, so that you do not need to specify an amount to extract the property.
The properties of a substance are accessed with the
(property of substance), which reads a multiplication expression
following it, so you may have to wrap it in parentheses.
Substances can be used in conversions, and can be added and multiplied
to transform them. Multiplication will change the amount of the
substance you have, so that you can write
kg egg to specify one
kilogram of eggs. Addition will combine certain properties (currently
molar_mass) to create a new substance entirely. Conversions of
substances allow you to get multiple results simultaneously, for
example if there are multiple different measurements of some property
of the substance available.
If the result of a calculation results in a substance, Rink will show all of the properties applicable for the given amount.
Index of Units
The full list of units is specified in the file
but a small list of the most helpful ones will be listed here. It is
intended that most units should be easy to guess the names of.
Official SI Derived Units
- Ohm (electrical resistance)
T(magnetic flux density)
- Mercury (Hg)
- Compounds and materials
- Water ice
- Silica glass
- Flint glass
- Pyrex glass
- Deuterium nucleus
- Helium nucleus
- Tritium nucleus
- Celestial bodies
- Earth's moon
- Crude oil
- Natural gas
- Heating oil
- Fuel oil
- Crude oil
- Clarified butter
- Cocoa butter
- Vegetable shortening
- Vegetable oil
- Olive oil
- Corn starch
- Heavy cream
- Sour cream
- Corn syrup
- Powdered sugar
- Brown sugar
- Baking powder
- Elements 1 through 118, by name (e.g.
- Speed of light
- Planck Constant
- Gravitational Constant
- Avogadro's number
- Gas Constant
- Boltzmann Constant
- Earth Gravity
- Earth Atmosphere Density
These are only enabled if Rink was compiled with support for currencies.
- EU Euro
- US dollar
- Japan yen
- Bulgaria lev
- Czech koruna
- Denmark kroner
- UK pound
- Hungary forint
- Poland złoty
- Romania lei
- Sweden krona
- Switzerland franc
- Norway krone
- Croatia kuna
- Russia ruble
- Turkey lira
- Australia dollar
- Brazil real
- Canada dollar
- PRC yuan
- Hong Kong dollar
- Indonesia rupiah
- Israel shekel
- India rupee
- South Korea won
- Mexico dollar
- Malaysia ringgit
- New Zealand dollar
- Phillipines piso
- Singapore dollar
- Thailand baht
- South Africa rand
Currently, all of these result in machine float fallback, because their results are real numbers that cannot be precisely represented as rationals.
sqrt(x): Square root, √x.
exp(x): The exponential function, e^x.
ln(x): The natural logarithm, log_e(x).
log(x,y): Logarithm in base y, log_y(x).
log2(x): Logarithm in base 2, log_2(x).
log10(x): Logarithm in base 10, log_10(x).
hypot(x,y): The length of the hypotenuse of a right-angle triangle given adjacent edges of length x and y.
sin(x): The sine function.
cos(x): The cosine function.
tan(x): The tangent function.
asin(x): Inverse sine, or arcsine.
acos(x): Inverse cosine, or arccosine.
atan(x): Inverse tangent, or arctangent.
atan2(x, y): Four-quadrant arctangent, which can be used to reverse sine+cosine back into an angle.
sinh(x): Hyperbolic sine.
cosh(x): Hyperbolic cosine.
tanh(x): Hyperbolic tangent.
asinh(x): Inverse hyperbolic sine function.
acosh(x): Inverse hyperbolic cosine function.
atanh(x): Inverse hyperbolic tangent function.