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Gradient with units

The unit of a gradient is the y-axis unit divided by the x-axis unit. Stating it correctly turns a bare number into a meaningful physical quantity.

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A gradient without a unit is only half an answer. Because the gradient is a change in the y-quantity divided by a change in the x-quantity, its unit is simply the y-axis unit divided by the x-axis unit.

For a graph of extension in centimetres against load in newtons, the gradient has the unit centimetre per newton, written cm per N. If the graph plotted velocity in metres per second against time in seconds, the gradient would be metres per second squared, which is acceleration.

Working out the unit this way is also a useful check on what the gradient physically represents. If the unit does not match the quantity you expected, it is a sign to review either the axes or the calculation.

Always quote the gradient as a number together with its derived unit, and give it to a sensible number of significant figures consistent with your data.

Load / N Extension / cm

What examiners award

Marks are awarded for deriving the gradient's unit as the y-axis unit over the x-axis unit and quoting the value with that unit.

Common mark losses

Marks are lost for giving the gradient as a bare number with no unit, or for stating a unit that does not match the two axes.

In short

The unit of a gradient is the y-axis unit divided by the x-axis unit. Stating it correctly turns a bare number into a meaningful physical quantity.

A routine that works

Practise the mechanics until they are automatic: label both axes with units, choose a scale that fills more than half the grid, plot points with a sharp pencil, draw a single best-fit line, and take the gradient from a large triangle with its coordinates and unit shown. One clean example beats re-reading the theory.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026

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