Moment of a force: M = F d
Moment of a force = force × distance normal to the direction of the force, or M = F d. M is the moment in newton metres (N m), F is the force in newtons (N) and d is the perpendicular distance from the pivot in metres (m). Separate Physics courses at all three boards include it, and the sheet in those exams prints it.
Equation
M = F d
| Symbol | Quantity | Unit |
|---|---|---|
M | moment | N·m |
F | force | N |
d | distance from pivot | m |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | M = F d |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Recall | M = F d |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Recall | M = F d |
| OCR Twenty First Century Physics B (J259) | Recall | M = F d |
Calculator: M = F d
What a moment is
A moment is the turning effect of a force. Doors, spanners, wheelbarrows and seesaws all turn about a fixed point called a pivot.
Two things make the turning effect bigger: a bigger force, or a force further from the pivot. That is why a door handle sits on the edge far from the hinges. Push near the hinge and the door hardly moves.
The distance must be measured at right angles to the line of the force. If you push at a slant, the useful distance is shorter than the length of the lever.
How the boards print it
- AQA Physics (8463): M = F d.
- Edexcel Physics (1PH0): the words only, moment of a force = force × distance normal to the direction of the force, with no symbol form.
- OCR Gateway Physics A (J249) and OCR Twenty First Century Physics B (J259): M = F d.
Moments are separate Physics content. Neither AQA Combined Science (8464) nor Edexcel Combined Science (1SC0) has this equation. The Edexcel equation list shows how it sits with Edexcel's other physics-only items.
All these courses mark it as a recall equation. From 2025 the exam gives you a sheet with it on anyway.
Balanced moments
When an object is balanced, the clockwise moments equal the anticlockwise moments about the pivot. On a seesaw, a heavy person close to the middle can balance a light person near the end.
So a balance question usually means two uses of M = F d. Work out the moment on one side, then set the other side equal to it and solve for the missing force or distance.
- F = M ÷ d
- d = M ÷ F
The force on each side is often a weight from W = m g. Pressure is the other physics-only equation that AQA and Edexcel leave out of Combined Science recall lists. The equation sheet guide compares the Physics and Combined Science lists.
Worked examples
M
- Change 80 cm to 0.8 m
- M = F d
- M = 30 × 0.8
- M = 24 N m
24 N m
F
- 25 cm = 0.25 m
- F = M ÷ d
- F = 40 ÷ 0.25
- F = 160 N
160 N
d
- A child on one side of a seesaw makes a moment of 350 N m. An adult of weight 500 N sits on the other side.
- d = M ÷ F
- d = 350 ÷ 500
- d = 0.7 m from the pivot
0.7 m
Common mistakes
- Measuring the distance to the wrong point. It runs from the pivot to the line of the force, not from one end of the object.
- Giving the answer in joules. A moment is measured in newton metres, N m.
- Leaving the lever length in centimetres, which makes the moment 100 times too large.
- Adding clockwise and anticlockwise moments together when the object balances. Set them equal instead.
Rearrange M = F d for force or distance in the Equation Rearranger.
Questions people ask
Why is a long spanner easier to use?
A longer handle puts your hand further from the nut. The same moment then needs a smaller force.
Is a moment in N m the same as energy in joules?
No. The units look alike, but a moment is a turning effect. Always write N m for a moment, never J.