How to Calculate the Accuracy of Measurements

Written by david chandler | 13/05/2017
How to Calculate the Accuracy of Measurements
Accurate and precise measurements are often required in many fields. (Lineal image by Ewe Degiampietro from

Calculating accuracy reveals how close a set of measurements are to an accepted reference value. This differs from precision, which describes how close the measurements are to each other. It is possible to have very precise measurements that are inaccurate. For example, if repeated measurements of a temperature are taken and each measurement is nearly identical, the results are considered precise. However, if these measurements are several degrees different from what the value should be, the results have low accuracy. Using a simple formula, the accuracy of measurements may be calculated.

Make a measurement using the appropriate instrument. For example, measuring the density of fresh water requires the volume and mass of a water sample to be taken and then the mass divided by the volume (density = mass/volume). If the mass of a 10.0ml sample of freshwater at 4 degrees Celsius (density varies slightly with temperature) measures 10.1 grams, then the density is 0.99 grams per cubic centimetre.

Reference the accepted value for the object being measured. Continuing the example, the reference density of fresh water at 4 degrees Celsius is 1.00g/cm3.

Subtract the measured value from the accepted value and then divide the difference by the accepted value. Multiply the quotient by 100 to produce the per cent error. The final formula appears as (measured value -- accepted value) ÷ accepted value x 100 = % error. Finishing the example, we find the per cent error of the measurement is one per cent ((0.99 -- 1.00)/1.00 x 100 = 1 %).

Things you need

  • Pencil
  • Paper
  • Measurement Data
  • Measurement Reference Value

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