Format units

format_units()

Given a number, a numerical vector, or a numerical column from a data frame, format_units() converts the numbers to character strings of the form,

    "a [u]" 

where a is the number and u is the measurement unit. The user can specify the number of significant digits.

Arguments.

• x   Vector to be formatted, of class numeric or class units. Can be a scalar, a vector, or a column from a data frame.

• digits   Numeric scalar, a positive integer. Applied as the digits argument of base::format(). Enough decimal places are included such that the smallest magnitude value has this many significant digits.

• unit   Character scalar, units label compatible with units package.

• unit_form   Character scalar. Possible values are “standard” (default) and “implicit” (implicit exponent form). In standard form, units are related with arithmetic symbols for multiplication, division, and powers, e.g., "kg/m^3" or "W/(m*K)". In implicit exponent form, symbols are separated by spaces and numbers represent exponents, e.g., "kg m-3" or "W m-1 K-1".

• big_mark   Character. Applied as the big.mark argument of base::format(). Default is "". If a period is selected for big_mark, the decimal mark is changed to a comma.

If you are writing your own script to follow along, we use these packages in this vignette:

library(formatdown)
library(data.table)
suppressPackageStartupMessages(library(units))
library(knitr)

Scalar

Assign a value and units,

x <- 101300
units(x) <- "Pa"

Use with inline R code.

`r format_units(x)`
`r format_units(x, unit = "hPa")`

which, in an .Rmd or .qmd document, are rendered as

• 101300 [Pa].
• 1013 [hPa].

Vector

The atmos data set included with formatdown has an altitude variable alt in meters. The columns do not include units metadata. Column is class numeric.

# Variable is class numeric
x <- atmos$alt
x
#> [1]     0 10000 20000 30000 40000 50000 60000 70000 80000
class(x)
#> [1] "numeric"

Assign measurement units to match the source values and format. Results are class character.

x_char <- format_units(x, unit = "m")
x_char
#> [1] "0 [m]"     "10000 [m]" "20000 [m]" "30000 [m]" "40000 [m]" "50000 [m]"
#> [7] "60000 [m]" "70000 [m]" "80000 [m]"

If we intend to convert the units, e.g., from meters to kilometers, we have to assign the source measurement units before using format_units(). Results are numeric, class units.

# Assign units before formatting
units(x) <- "m"
x
#> Units: [m]
#> [1]     0 10000 20000 30000 40000 50000 60000 70000 80000
class(x)
#> [1] "units"

Convert units and format. The numbers change to match the unit conversion. Results are class character.

# Covert units and format as character
x_char <- format_units(x, unit = "km")
x_char
#> [1] "0 [km]"  "10 [km]" "20 [km]" "30 [km]" "40 [km]" "50 [km]" "60 [km]"
#> [8] "70 [km]" "80 [km]"

Digits

The digits argument sets the number of significant digits. Here, temperature values (K) are reported to 4 significant digits.

x <- sort(atmos$temp, decreasing = TRUE)
format_units(x, digits = 4, unit = "K")
#> [1] "288.1 [K]" "270.6 [K]" "250.3 [K]" "247.0 [K]" "226.5 [K]" "223.2 [K]"
#> [7] "219.6 [K]" "216.7 [K]" "198.6 [K]"

With values in decimal form, reducing digits to 3 has the expected effect of rounding to the units place.

format_units(x, digits = 3, unit = "K")
#> [1] "288 [K]" "271 [K]" "250 [K]" "247 [K]" "227 [K]" "223 [K]" "220 [K]"
#> [8] "217 [K]" "199 [K]"

However, reducing digits to 2 has no additional effect. To reduce the number of significant digits further, we apply signif() to the numerical values before formatting with format_units().

# Values are not converted to 2 significant digits
format_units(x, digits = 2, unit = "K")
#> [1] "288 [K]" "271 [K]" "250 [K]" "247 [K]" "227 [K]" "223 [K]" "220 [K]"
#> [8] "217 [K]" "199 [K]"

# Apply signif() before formatting
format_units(signif(x, 2), unit = "K")
#> [1] "290 [K]" "270 [K]" "250 [K]" "250 [K]" "230 [K]" "220 [K]" "220 [K]"
#> [8] "220 [K]" "200 [K]"

If values span different orders of magnitude, the number of significant digits is applied to the smallest magnitude value and the number of decimal places in the other values is set to match.

For example, from the metals data set included with formatdown, the elastic modulus values (Pa) are converted to (GPa) with digits = 3.

x <- sort(metals$elast_mod, decreasing = TRUE)
units(x) <- "Pa"
format_units(x, digits = 3, unit = "GPa")
#> [1] "206.8 [GPa]" "146.9 [GPa]" "117.2 [GPa]" "102.0 [GPa]" "73.1 [GPa]" 
#> [6] "13.8 [GPa]"

Three digits applied to the smallest magnitude value yields “13.8 [GPa]”. Larger values are then formatted to the same number of decimal places. Thus some larger values will have more than three digits, e.g., “206.8 [GPa]”.

Data frame

Using the atmos data set include with formatdown with various atmospheric properties as a function of height above sea level.

# Data set included with formatdown
DT <- copy(atmos)

# Render in document
knitr::kable(DT, align = "r")

Formatting one column at a time, assigning and converting units, and assigning significant digits ad-hoc. When numerical values in a column span a number of orders of magnitude, the number in the column with the smallest magnitude, e.g., pressure or density last row, is displayed with the number of significant digits specified by the digits argument.

units(DT$alt) <- "m"
DT[, alt := format_units(alt, unit = "km")]

units(DT$temp) <- "K"
DT[, temp := format_units(temp, 3, unit = "deg_C")]

units(DT$pres) <- "Pa"
DT[, pres := format_units(pres, unit = "hPa")]

units(DT$dens) <- "kg/m^3"
DT[, dens := format_units(dens, unit = "g/m^3", unit_form = "implicit")]

units(DT$sound) <- "m/s"
DT[, sound := format_units(sound, 4)]

knitr::kable(
  DT,
  align = "r",
  col.names = c("Altitude", "Temperature", "Pressure", "Density", "Speed of sound")
)

US customary units

The same table can be formatted in US customary units as shown below.

# Data set included with formatdown
DT <- copy(atmos)

units(DT$alt) <- "m"
DT[, alt := format_units(alt, unit = "ft")]

units(DT$temp) <- "K"
DT[, temp := format_units(temp, 2, unit = "deg_F")]

units(DT$pres) <- "Pa"
DT[, pres := format_units(pres, unit = "psi")]

units(DT$dens) <- "kg/m^3"
DT[, dens := format_units(dens, unit = "lb/ft^3", unit_form = "implicit")]

units(DT$sound) <- "m/s"
DT[, sound := format_units(sound, 4, unit = "ft/s")]

knitr::kable(
  DT,
  align = "r",
  col.names = c("Altitude", "Temperature", "Pressure", "Density", "Speed of sound")
)

Applying powers of ten notation

Power of ten notation can often be avoided by applying the units format, but in some cases both may be desired. For example, the column of density values in the table above span several orders of magnitude. One might wish to format these values using power of ten notation.

Our approach is to work with the original data for this one column only and substitute the result for the “Density” column in the data frame above.

# Start with the original density vector
x <- atmos$dens

# Assign the original units
units(x) <- "kg/m^3"

# Display a representative value
x[5]
#> 0.004 [kg/m^3]

We use the units() function to convert to the units we want, in this case, [lb ft-3] (using the units package “implicit” style of notation).

# Convert to US Customary units
display_units <- "lb ft-3"
units(x) <- display_units

# Display the same representative value
x[5]
#> 0.0002497118 [lb/ft^3]

Having already assigned our units to the display_units variable (for later use), we convert the vector from units class to numeric class.

# Convert the vector to numeric values
x <- as.numeric(x)

# Display the representative value
x[5]
#> [1] 0.0002497118

Apply format_power() to yield the values as character strings in power of ten notation.

# Apply power of ten notation using format_power()
x <- format_power(x, digits = 3, format = "sci")

# Display the representative value
x[5]
#> [1] "$\\large 2.50 \\times 10^{-4}$"

Append the display units to each element of the vector.

# Append units string to value strings
x <- paste0(x, " [", display_units, "]")

# Display the representative value
x[5]
#> [1] "$\\large 2.50 \\times 10^{-4}$ [lb ft-3]"

Finally, substitute this vector for the column of density values constructed earlier.

# Substitute for column in the data frame from above
DT[, dens := x]

knitr::kable(
  DT,
  align = "r",
  col.names = c("Altitude", "Temperature", "Pressure", "Density", "Speed of sound")
)