math.uncertainty

measurements with an error, 5 ± 0.1 m, carried through arithmetic

Example results generated on 2026-10-08. Ones using now, today or randomness will differ when you run them: press Run on any example to run it in your browser, after editing it if you like.

operators

# x ± e (or x +- e)
5 ± 0.1 m
# x ± n%
20 ± 5%
# → 20 ± 1

pretty

# long: value's best prefix for both, separators
pretty(1500 ± 20 m)
# → "1.5 ± 0.02 km"
# short: same, K M B T
pretty(1234567 ± 1000, "short")
# → "1.23M ± 1K"

propagation

# errors add in quadrature
(5 ± 0.3) + (2 ± 0.4)
# → 7 ± 0.5
# relative errors too
(10 ± 1 m) * (2 ± 0.1 m)
# → 20 ± 2.23607 m^2
# through functions
sqrt(16 ± 1)
# → 4 ± 0.125
# and conversions
5 ± 0.1 km to mi
# → 3.10686 ± 0.0621371 mi

Functions

value

value(x: uncertain): the central value, dropping the uncertainty

(5 ± 0.1 m).value
# → 5 m

See also: error

error

error(x: uncertain): the uncertainty, in the same unit

(5 ± 0.1 m).error
# → 0.1 m
(20 ± 5%).error
# → 1

See also: value

More examples

uncertainty

# area of a measured rectangle
(2 ± 0.05 m) * (3 ± 0.05 m)
# → 6 ± 0.180278 m^2
# pendulum period from its length in m
2 * pi * sqrt((1 ± 0.01) / 9.81)
# → 2.00607 ± 0.0100303