Error Propagation

Say, for example, that we have measured a rectangle to be 11 +/- 0.4 centimeters wide and 8 +/- 0.3 centimeters long. We can then calculate the area with uncertainty as follows:

from measurement_stats import ValueUncertainty

width = ValueUncertainty(11, 0.4)
length = ValueUncertainty(8, 0.3)

area = length * width

print('AREA:', area.label)
# $ AREA: 88 +/- 5

For a more complicated example, consider the canonical physics 101 experiment of trying to calculate the acceleration due to gravity using a pendulum. If a student has setup a pendulum with a measured length of 92.95 centimeters and an uncertainty of 0.1 centimeters and measured a period of that pendulum to be 1.936 seconds with an uncertainty of 0.004 seconds, the acceleration due to gravity, with propagated uncertainty, can be determined as follows:

from measurement_stats import ValueUncertainty

l = ValueUncertainty(92.95, 0.1)
T = ValueUncertainty(1.936, 0.004)

g = 4.0 * (math.pi ** 2) * l / (T ** 2)

print('Acceleration Due To Gravity:', g.label)
# $ Acceleration Due To Gravity: 979 +/- 4