Uncertainty and Errors in GCSE Science Practicals: How to Calculate and Reduce Them

What is the difference between an error and a mistake?

In everyday language, "error" and "mistake" are interchangeable, but in science they mean different things. A mistake (or blunder) is a human error that can be avoided — misreading a scale, recording the wrong number, or knocking apparatus. Mistakes should be identified and the measurement repeated.

An error is an unavoidable limitation of the measurement process itself. Even with perfect technique and attention, errors exist because no instrument is perfect and no condition is perfectly controlled. Errors fall into two types: random and systematic.

What is the difference between random and systematic errors?

How do you calculate absolute uncertainty?

The absolute uncertainty of a single measurement made with an analogue instrument is half the smallest scale division:

Absolute uncertainty = ½ × smallest scale division

Example 1 — ruler: A standard 30 cm ruler has smallest divisions of 1 mm (0.1 cm). The absolute uncertainty is ±0.5 mm (±0.05 cm).

If you measure a piece of string by placing it against the ruler, you take two readings (start and end positions), so the absolute uncertainty in the length is:

0.5 mm + 0.5 mm = ±1 mm

Example 2 — thermometer: A thermometer with 1 °C divisions has an absolute uncertainty of ±0.5 °C. If you measure a temperature rise from 20 °C to 45 °C, the absolute uncertainty in the temperature change is ±0.5 + ±0.5 = ±1 °C.

How do you calculate percentage uncertainty step by step?

1. Identify the measurement and its absolute uncertainty. Record the value you measured and the absolute uncertainty of the instrument used.

2. Apply the formula. Percentage uncertainty = (absolute uncertainty ÷ measured value) × 100

3. Substitute your values. If you measured a length of 45 mm with a ruler (absolute uncertainty ±0.5 mm): percentage uncertainty = (0.5 ÷ 45) × 100 = 1.1%

4. For a derived quantity, add percentage uncertainties. When you calculate a result by multiplying or dividing measurements, add the percentage uncertainties of each measurement together. For example, if speed = distance ÷ time and distance has 2% uncertainty while time has 3% uncertainty, the percentage uncertainty in speed is 2 + 3 = 5%.

5. Express the final result with uncertainty. Write the result as: measured value ± absolute uncertainty in the result. Convert back if needed: if speed = 3.0 m/s and percentage uncertainty = 5%, absolute uncertainty = 5% of 3.0 = 0.15 m/s, so result = 3.0 ± 0.2 m/s (rounded to 1 significant figure for the uncertainty).

Worked example: comparing uncertainty in two thermometers

A student measures the boiling point of water twice using two different thermometers:

The digital thermometer has a much smaller percentage uncertainty. However, if the digital thermometer has not been calibrated and reads 1 °C too high (a systematic error), its readings are systematically wrong despite the low uncertainty — demonstrating that low uncertainty does not mean high accuracy if systematic errors are present.

How do you reduce random errors?

• Take more repeats and calculate the mean. Random errors cancel out statistically — some readings will be above the true value and some below, and the mean closes in on the true value.
• Use instruments with smaller scale divisions to reduce the absolute uncertainty of individual readings.
• Control variables carefully — for example, shielding apparatus from draughts, using a water bath to maintain constant temperature, and clamping apparatus so it does not move.
• Use a set square when reading a scale to ensure the eye is directly level with the measurement, eliminating parallax error.

How do you reduce systematic errors?

• Calibrate your instruments against a known standard before use. For example, check a thermometer reads 0 °C in ice water and 100 °C in boiling water.
• Correct for zero errors. If a balance reads 0.2 g with nothing on it, subtract 0.2 g from every reading.
• Ensure consistent technique. Always read analogue scales from directly in front (to avoid parallax), at the same point in an oscillation (for a pendulum), or at the same angle.
• Use control experiments to identify systematic sources of bias, such as background radiation in a radioactivity practical.

Frequently asked questions

Q: What is accuracy and how is it different from precision?

Accuracy describes how close a measurement is to the true value; it is affected mainly by systematic errors. Precision describes how reproducible measurements are — a precise instrument gives consistent readings with low scatter, even if they are all wrong in the same direction. Ideally you want both accuracy and precision, but a precise instrument with a systematic error gives precise but inaccurate results.

Q: Do I need to worry about uncertainty in biology practicals?

Yes — uncertainty applies in all three sciences. In biology, common sources include reading the scale on a measuring cylinder, timing an experiment by hand (reaction time is a random error), or measuring a length under a microscope. For enzyme rate experiments, the uncertainty in temperature measurement and timing both contribute to the percentage uncertainty in the calculated rate.

Q: When should I round uncertainty values?

Uncertainties are conventionally rounded to one significant figure. The measurement itself should then be quoted to the same decimal place as the uncertainty. For example: if a calculation gives 4.56 ± 0.23 m, round to 4.6 ± 0.2 m. This avoids implying more precision than the uncertainty allows.

Q: How do I spot a systematic error from a graph?

On a graph of results, a systematic error often appears as a non-zero y-intercept when theory predicts zero, or as a parallel shift of the data from the expected line. Random errors appear as scatter around the line of best fit. If the line of best fit passes through the origin as expected but individual points scatter around it, random errors dominate. If the line is parallel to the expected one but offset, a systematic error is present.

Q: Can I remove a systematic error by taking more readings?

No. A systematic error shifts every measurement in the same direction by the same amount, so taking more readings and averaging them gives you a more precise estimate of the wrong value. The only way to remove a systematic error is to identify its source — a miscalibrated instrument, an incorrect zero, or a consistently biased technique — and correct it.

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