R has little support for physical measurement units. The exception is formed by time differences: time differences objects of class difftime have a units attribute that can be modified:

t1 = Sys.time() 
t2 = t1 + 3600 
d = t2 - t1
class(d)
## [1] "difftime"
units(d)
## [1] "hours"
d
## Time difference of 1 hours
units(d) = "secs"
d
## Time difference of 3600 secs

We see here that the units method is used to retrieve and modify the unit of time differences.

This idea can be generalized to other physical units. The units package, presented here, does this, and builds upon the udunits2 R package, which in turn is build upon the udunits2 C library. The udunits2 library provides the following operations:

Th units R package uses R package udunits2 to extend R with functionality for manipulating numeric vectors that have physical measurement units associated with them, in a similar way as difftime objects behave.

Setting units, unit conversion

Units must be defined before they are used. Units are defined from a string but by explicitly defining units before they are used we avoid having new units in use due to misspellings. A unit is defined using the make_units function

library(units)
m <- make_unit("m")
s <- make_unit("s")

The objects created,

m
## 1 m

represent a single value of the named quantity (``m’’). To obtain different quantities of named units, we use them in expressions such as

(a <- 1:10 * m/s)
## Units: m/s
##  [1]  1  2  3  4  5  6  7  8  9 10

the result, e.g.

a[10]
## 10 m/s

literally means “10 times 1 m divided by 1 s”. In writing, the “1” values are omitted, and the multiplication is implicit.

The units package comes with a list of over 3000 predefined units, which can be used without calling make_unit. One way of making this list available would be to attach it, but this leads to a number of name conflicts: T (for tesla) wound mask the value that otherwise refers to TRUE, .

A cleaner approach is to use with, as in

rm(m) ; rm(s)
with(ud_units, 1:10 * m/s)
## Units: m/s
##  [1]  1  2  3  4  5  6  7  8  9 10

When conversion is meaningful, such as hours to seconds or meters to kilometers, conversion can be done explicitly by setting the units of a vector

b = a
units(b) <- with(ud_units, km/h)
b
## Units: km/h
##  [1]  3.6  7.2 10.8 14.4 18.0 21.6 25.2 28.8 32.4 36.0

Basic manipulations

Arithmetic operations

Arithmetic operations verify units, and create new ones

a + a
## Units: m/s
##  [1]  2  4  6  8 10 12 14 16 18 20
a * a
## Units: m^2/s^2
##  [1]   1   4   9  16  25  36  49  64  81 100
a ^ 2
## Units: m^2/s^2
##  [1]   1   4   9  16  25  36  49  64  81 100
a ** -2
## Units: s^2/m^2
##  [1] 1.00000000 0.25000000 0.11111111 0.06250000 0.04000000 0.02777778
##  [7] 0.02040816 0.01562500 0.01234568 0.01000000

and convert to the units of the first argument if necessary:

a + b # m/s + km/h -> m/s
## Units: m/s
##  [1]  2  4  6  8 10 12 14 16 18 20

Currently, powers are only supported for integer powers, so using a ** 2.5 would result in an error.

There are some basic simplification of units:

t <- with(ud_units, s)
a * t
## Units: m
##  [1]  1  2  3  4  5  6  7  8  9 10

which also work when units need to be converted before they can be simplified:

t <- with(ud_units, min)
a * t
## Units: m
##  [1]  60 120 180 240 300 360 420 480 540 600

Simplification to unit-less values gives the “1” as unit:

m <- with(ud_units, m)
a * t / m
## Units: 1
##  [1]  60 120 180 240 300 360 420 480 540 600

Allowed operations that require convertible units are +, -, ==, !=, <, >, <=, >=. Operations that lead to new units are *, /, and the power operations ** and ^.

Mathematical functions

Mathematical operations allowed are: abs, sign, floor, ceiling, trunc, round, signif, log, cumsum, cummax, cummin.

signif(a ** 2 / 3, 3)
## Units: m^2/s^2
##  [1]  0.333  1.330  3.000  5.330  8.330 12.000 16.300 21.300 27.000 33.300
cumsum(a)
## Units: m/s
##  [1]  1  3  6 10 15 21 28 36 45 55
log(a) # base defaults to exp(1)
## Units: ln(m/s)
##  [1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379 1.7917595 1.9459101
##  [8] 2.0794415 2.1972246 2.3025851
log(a, base = 10)
## Units: lg(m/s)
##  [1] 0.0000000 0.3010300 0.4771213 0.6020600 0.6989700 0.7781513 0.8450980
##  [8] 0.9030900 0.9542425 1.0000000
log(a, base = 2)
## Units: lb(m/s)
##  [1] 0.000000 1.000000 1.584963 2.000000 2.321928 2.584963 2.807355
##  [8] 3.000000 3.169925 3.321928

Summary functions

Summary functions sum, min, max, and range are allowed:

sum(a)
## 55 m/s
min(a)
## 1 m/s
max(a)
## 10 m/s
range(a)
## Units: m/s
## [1]  1 10
with(ud_units, min(m/s, km/h)) # converts to first unit:
## 0.2777778 m/s

Printing

Following difftime, printing behaves differently for length-one vectors:

a
## Units: m/s
##  [1]  1  2  3  4  5  6  7  8  9 10
a[1]
## 1 m/s

Subsetting

The usual subsetting rules work:

a[2:5]
## Units: m/s
## [1] 2 3 4 5
a[-(1:9)]
## 10 m/s

Concatenation

c(a,a)
## Units: m/s
##  [1]  1  2  3  4  5  6  7  8  9 10  1  2  3  4  5  6  7  8  9 10

concatenation converts to the units of the first argument, if necessary:

c(a,b) # m/s, km/h -> m/s
## Units: m/s
##  [1]  1  2  3  4  5  6  7  8  9 10  1  2  3  4  5  6  7  8  9 10
c(b,a) # km/h, m/s -> km/h
## Units: km/h
##  [1]  3.6  7.2 10.8 14.4 18.0 21.6 25.2 28.8 32.4 36.0  3.6  7.2 10.8 14.4
## [15] 18.0 21.6 25.2 28.8 32.4 36.0

Conversion to/from difftime

From difftime to units:

t1 = Sys.time() 
t2 = t1 + 3600 
d = t2 - t1
du <- as.units(d)

vice versa:

dt = as.dt(du)
class(dt)
## [1] "difftime"
dt
## Time difference of 1 hours

units in matrix objects

with(ud_units, matrix(1:4,2,2) * m/s)
## Units: m/s
##      [,1] [,2]
## [1,]    1    3
## [2,]    2    4
with(ud_units, matrix(1:4,2,2) * m/s * 4 * m/s)
## Units: m^2/s^2
##      [,1] [,2]
## [1,]    4   12
## [2,]    8   16

but

with(ud_units, (matrix(1:4,2,2) * m/s) %*% (4:3 * m/s))
##      [,1]
## [1,]   13
## [2,]   20

strips units.

units objects in data.frames

units in data.frame objects are printed, but do not appear in summary:.

set.seed(131)
d <- with(ud_units,
         data.frame(x = runif(4), 
                    y = runif(4) * s, 
                    z = 1:4 * m/s))
d
##           x           y     z
## 1 0.2064370 0.8463468 s 1 m/s
## 2 0.1249422 0.5292048 s 2 m/s
## 3 0.2932732 0.5186254 s 3 m/s
## 4 0.3757797 0.2378545 s 4 m/s
summary(d)
##        x                y                z       
##  Min.   :0.1249   Min.   :0.2379   Min.   :1.00  
##  1st Qu.:0.1861   1st Qu.:0.4484   1st Qu.:1.75  
##  Median :0.2499   Median :0.5239   Median :2.50  
##  Mean   :0.2501   Mean   :0.5330   Mean   :2.50  
##  3rd Qu.:0.3139   3rd Qu.:0.6085   3rd Qu.:3.25  
##  Max.   :0.3758   Max.   :0.8463   Max.   :4.00
d$yz = with(d, y * z)
d
##           x           y     z          yz
## 1 0.2064370 0.8463468 s 1 m/s 0.8463468 m
## 2 0.1249422 0.5292048 s 2 m/s 1.0584095 m
## 3 0.2932732 0.5186254 s 3 m/s 1.5558761 m
## 4 0.3757797 0.2378545 s 4 m/s 0.9514180 m
d[1, "yz"]
## 0.8463468 m

formatting

Units are often written in the form m2 s-1, for square meter per second. This can be defined as unit, but is not interpreted by R:

(x = 1:10 * make_unit("m2 s-1"))
## Units: (m2 s-1)
##  [1]  1  2  3  4  5  6  7  8  9 10

udunits understands such string, and can convert them

y = 1:10 * with(ud_units, m^2/s)
x + y
## Units: (m2 s-1)
##  [1]  2  4  6  8 10 12 14 16 18 20

but R cannot simplify them:

x/y
## Units: (m2 s-1)*s/m^2
##  [1] 1 1 1 1 1 1 1 1 1 1

Instead, we can tell R to parse such a string, which then allows simplification:

(z = 1:10 * parse_unit("m2 s-1"))
## Units: m^2/s
##  [1]  1  2  3  4  5  6  7  8  9 10
z + y
## Units: m^2/s
##  [1]  2  4  6  8 10 12 14 16 18 20
z / y
## Units: 1
##  [1] 1 1 1 1 1 1 1 1 1 1

Printing units in this form is done by

as_cf(z)
## [1] "m2 s-1"

plotting

Base scatter plots and histograms support automatic unit placement in axis labels. In the following example we first convert to SI units. (Unit in needs a bit special treatment, because in is a reserved word in R.)

mar = par("mar") + c(0, .3, 0, 0)
displacement = mtcars$disp * ud_units[["in"]]^3
units(displacement) = with(ud_units, cm^3)
weight = mtcars$wt * 1000 * with(ud_units, lb)
units(weight) = with(ud_units, kg)
par(mar = mar)
plot(weight, displacement)

We can change grouping symbols from [ ] into ( ):

units_options(group = c("(", ")") )  # parenthesis instead of square brackets
par(mar = mar)
plot(weight, displacement)

We can also remove grouping symbols, increase space between variable name and unit by:

units_options(sep = c("~~~", "~"), group = c("", ""))  # no brackets; extra space
par(mar = mar)
plot(weight, displacement)

More complex units can be plotted either with negative powers, or as divisions, by modifying one of units’s global options using units_options:

gallon = make_unit("gallon")
consumption = mtcars$mpg * with(ud_units, mi/gallon)
units(consumption) = with(ud_units, km/l)
par(mar = mar)
plot(displacement, consumption) # division in consumption

units_options(negative_power = TRUE) # division becomes ^-1
plot(displacement, consumption) # division in consumption

As usual, units modify automatically in expressions:

units_options(negative_power = TRUE) # division becomes ^-1
par(mar = mar)
plot(displacement, consumption)

plot(1/displacement, 1/consumption)