Absolute Uncertainty Calculator

Calculate absolute uncertainty from your dataset with step-by-step working and clear statistical interpretation.

Quick Facts

Method
Absolute uncertainty = (max − min) / 2, reported as mean ± uncertainty
Same units as the measurement; divide by the mean for relative and percentage uncertainty.

Your Results

Calculated
Result
-
Mean ± absolute uncertainty
Absolute uncertainty
-
Half the range (max − min) / 2
Relative uncertainty
-
Uncertainty ÷ mean
Percentage uncertainty
-
Relative × 100%

Ready

Enter your repeated readings and press Calculate.

What absolute uncertainty means

Every measurement has a limited precision, so no single reading is exactly the true value. The absolute uncertainty is the size of that doubt, quoted in the same units as the measurement. If a length is written as 24.5 ± 0.2 cm, the "0.2 cm" is the absolute uncertainty: the true length is expected to lie somewhere between 24.3 cm and 24.7 cm. Absolute uncertainty always carries units (cm, g, s, V), which is what distinguishes it from relative or percentage uncertainty, both of which are dimensionless.

The formula this calculator uses

When you take several repeated readings of the same quantity, the standard classroom and lab method is to use the mean as the best estimate and half the range as the absolute uncertainty:

  • Best estimate = mean = (sum of readings) ÷ n
  • Absolute uncertainty = (largest reading − smallest reading) ÷ 2
  • Relative (fractional) uncertainty = absolute uncertainty ÷ mean
  • Percentage uncertainty = relative uncertainty × 100%

The result is reported as mean ± absolute uncertainty. Half the range is used because the true value should sit within ± half the spread of the readings around their centre. For the default data (24.3, 24.6, 24.4, 24.5, 24.2 cm): the mean is 24.4 cm, the range is 24.6 − 24.2 = 0.4 cm, so the absolute uncertainty is 0.2 cm, giving 24.4 ± 0.2 cm. The percentage uncertainty is 0.2 ÷ 24.4 × 100 ≈ 0.82%.

Absolute vs. relative vs. percentage uncertainty

These three are just different ways of expressing the same doubt. Absolute uncertainty keeps the units and answers "how many centimetres could I be off?". Relative uncertainty removes the units by dividing by the measured value, which lets you compare the quality of measurements made on different scales. Percentage uncertainty is simply the relative uncertainty times 100. A ±0.2 cm error is large on a 2 cm object (10%) but tiny on a 200 cm object (0.1%), even though the absolute value is identical — that is exactly why relative and percentage figures exist.

Reporting and significant figures

Convention is to quote the absolute uncertainty to one significant figure (occasionally two for very precise work), then round the measured value to the same decimal place as the uncertainty. So 24.4267 ± 0.2 cm is written 24.4 ± 0.2 cm, not 24.4267 ± 0.2 cm — the extra digits are meaningless once you admit uncertainty in the first decimal.

Frequently Asked Questions

What is absolute uncertainty in simple terms?
It is the amount by which your measurement could be wrong, written in the same units as the measurement. Reporting a mass as 50.0 ± 0.5 g means the true mass is expected to be between 49.5 g and 50.5 g; the 0.5 g is the absolute uncertainty.
Why is the uncertainty half the range and not the full range?
The mean sits roughly in the middle of the readings, so the true value should lie within about ± half the total spread of those readings. Taking half the range (max − min divided by 2) gives a symmetric ± value around the mean. This is a quick, widely taught estimate; for larger data sets many people instead use the standard deviation or the standard error of the mean.
How do I turn absolute uncertainty into percentage uncertainty?
Divide the absolute uncertainty by the measured value (the mean), then multiply by 100. For 24.4 ± 0.2 cm: 0.2 ÷ 24.4 × 100 ≈ 0.82%. To go the other way, multiply the percentage uncertainty (as a decimal) by the measured value: 0.82% of 24.4 cm gives back 0.2 cm.
What if I only have a single reading?
The half-range method needs at least two readings. For a single reading, the absolute uncertainty is usually taken from the instrument's resolution — for a digital scale, ± the last displayed digit; for an analogue scale, typically ± half the smallest division. This calculator is designed for repeated readings, so enter two or more values.

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