Absolute Uncertainty Calculator

Absolute uncertainty is the margin by which a measured value may differ from the true value. It is expressed in the same units as the measurement itself — for example, if you measure 150 g with an absolute uncertainty of 7.5 g, the true value lies somewhere between 142.5 g and 157.5 g. It quantifies the precision limit of your measuring instrument or method.

The formula is: Absolute Uncertainty (AU) = Measured Value (MV) × (Relative Uncertainty / 100). So if your measured value is 150 and the relative uncertainty is 5%, the absolute uncertainty is 150 × 5/100 = 7.5. This same relationship lets you convert between the two forms of uncertainty.

Multiply your measured value by the relative uncertainty expressed as a decimal. For instance, a relative uncertainty of 3% on a measurement of 200 gives an absolute uncertainty of 200 × 0.03 = 6. The result tells you the actual ± range around your measurement.

Absolute uncertainty is expressed in the same units as the measurement (e.g. ±0.5 s), while relative uncertainty is a dimensionless ratio — usually shown as a percentage — of the absolute uncertainty to the measured value (e.g. 2%). Relative uncertainty is useful for comparing precision across measurements of different magnitudes, whereas absolute uncertainty is used when reporting a result.

Use the formula: AU = Measured Value × (Relative Uncertainty % / 100). For example, if a voltage reading is 12 V with a 4% relative uncertainty, the absolute uncertainty is 12 × 0.04 = 0.48 V, so the result is reported as 12 ± 0.48 V.

Technically yes, though it would indicate an extremely imprecise measurement — one where the true value could even be zero or negative. In practice, if your absolute uncertainty approaches or exceeds the measured value, it signals that the measurement method or instrument is not suitable for the task.

When reporting experimental results, scientists write the measured value alongside its absolute uncertainty, for example: 9.81 ± 0.05 m/s². This tells the reader both the best estimate and the range within which the true value is expected to fall, accounting for instrument precision and human error.

Suppose a coach uses a stopwatch with a precision of ±0.01 s, but human reaction time adds about ±0.5 s. The absolute uncertainty of the time measurement is dominated by human reaction time — roughly ±0.5 s — not the device precision. This illustrates that absolute uncertainty accounts for all sources of error, not just instrumental ones.