Revision summary

A measurement needs a clear quantity, a sensible unit and a method suitable for the object or event. Use the links below when you need the reasoning behind a rule.

Base quantities and units

A quantity symbol describes the variable; a unit symbol identifies its unit. In l = 2.0 m, lowercase l means length and m means metre. Kelvin is K, without a degree sign.

Prefixes and conversions

For area, square the length conversion factor; for volume, cube it. Check the order of size before accepting a result: a hair is much thinner than a coin.

Choose an instrument

• Range: can it cover the measurement?
• Resolution: are its divisions or display steps small enough?
• Method: can it be aligned, read and used without distorting the object?

Precision concerns agreement between repeats; accuracy concerns closeness to the true or accepted value. More displayed digits alone guarantee neither.

Read, correct and calculate

Length from a rule

Final end reading - initial end reading. Look perpendicularly at the scale to avoid parallax.

Stable zero offset

Corrected reading = displayed reading - signed zero offset. Repeating alone does not remove the offset.

Period of a repeated motion

Mean elapsed time for N complete oscillations / N. Use the same reference point and direction for each count.

Volume by displacement

Final water volume - initial water volume. Fully submerge a suitable solid; avoid trapped air and lost water. Read the lower water meniscus at eye level.

Use quantity/unit headings in data tables. Record readings consistently with the instrument; preserve the original observations when averaging or correcting. The measurement-method directory links to examples for motion, forces, thermal changes, waves, optics, circuits and radioactivity.

Practical skills

• Readings: record to the instrument's precision, such as 12.0 cm on a millimetre rule.
• Tables: heading = quantity / unit; at least 5 sets of readings over a wide range.
• Calculated values: same number of significant figures as the least precise reading, or one more.
• Graphs: labelled axes with units, an easy scale (1, 2 or 5 per square, never 3, 6 or 7), points filling half the grid, one thin best-fit line.
• Gradient: a triangle using more than half the line, corners read from the line, answer with a unit.
• Errors: name a specific source of error and an improvement that fixes it.
• Plans: variables, apparatus, procedure, range, table and graph, risks and precautions. See the worked plan.

Scalars and vectors

• Scalars have magnitude only: distance, speed, mass, time, temperature and energy.
• Vectors have magnitude and direction: displacement, velocity, acceleration and force, including weight.
• A negative value alone does not make a quantity a vector. State a vector's direction or the chosen positive direction.

Pure: add two vectors graphically

1. Choose and state a useful scale.
2. Draw both vectors head to tail, preserving their magnitudes and directions.
3. Draw the resultant from the first tail to the final head.
4. Measure its length and direction; convert the length back using the scale.

Use a paper construction for physical ruler measurements. A resized screen image does not preserve centimetres.