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Horizontal component of a force Formula, SPM Physics

Formula: Fₓ = F cos θ. Not given in the exam, recall it.

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Horizontal component of a force
Fₓ = F cos θ

Not given in the exam, recall it.

What it is for

Horizontal component of a force is used in Force and Motion II (SPM Physics Form 5). Keep the SI units in every line of working. Force and Motion II

Symbols and SI units

SymbolMeaningSI unit
Fₓhorizontal component of forceN
FforceN
θangle to the horizontal°

Rearrangements

  • F = Fₓ / cos θ
  • cos θ = Fₓ / F

Worked example

A force F = 50 N acts at θ = 30° to the horizontal. Fₓ = F cos θ = 50 × cos 30° = 50 × 0.866 = 43.3 N.

Common trap

Use cos for the component adjacent to the angle (usually horizontal). Measure θ from the horizontal.

Understanding the horizontal component of a force

The formula Fₓ = F cos θ resolves a force into its horizontal part. Fₓ is the horizontal component, measured in newtons (N). F is the full force, also in newtons. θ is the angle the force makes with the horizontal, in degrees (°).

Cosine appears because the horizontal side is adjacent to the angle. As θ grows, cos θ shrinks, so less of the force acts horizontally, a force pointing almost straight up has a tiny horizontal component.

Rearrange when needed: F = Fₓ / cos θ recovers the full force from its horizontal part, and cos θ = Fₓ / F gives the angle. Make sure the calculator is in degree mode and that θ is measured from the horizontal, not the vertical.

A worked example, step by step

A rope pulls a crate with a force F = 120 N at θ = 40° above the horizontal ground. Find the horizontal component that drags the crate forward.

Apply the formula with units:

  • Fₓ = F cos θ = 120 N × cos 40°
  • Fₓ = 120 N × 0.766 = 91.9 N

So the horizontal pull is Fₓ = 91.9 N (3 significant figures). Only this part moves the crate along the ground; the rest of the 120 N lifts it slightly.

As a sanity check, Fₓ (91.9 N) is smaller than F (120 N), as it must be, a component can never exceed the whole force.

Common mistakes and how this is tested

The main trap: use cos for the component adjacent to the angle (usually horizontal), and measure θ from the horizontal.

Other common errors:

  • Swapping cos and sin, which gives the vertical component instead.
  • Leaving the calculator in radian mode, so cos 40° comes out wrong.
  • Measuring the angle from the vertical without adjusting the formula.

Questions ask you to calculate the horizontal component of a pull or push, to define resolution of forces, or to explain why only the horizontal part does the work of moving an object across level ground.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

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

Frequently asked questions

Is this formula given in the exam?
No. SPM Physics papers provide no formula sheet, so this must be recalled.
When is the horizontal component largest?
When θ = 0°, so the force is horizontal and cos 0° = 1, giving Fₓ = F. The whole force then acts horizontally and none is wasted lifting or pressing down.
What if the angle is measured from the vertical?
Then the horizontal component uses sine instead: Fₓ = F sin θ. Always identify which side of the angle is horizontal before choosing cos or sin.
Do the two components add back to F?
Not by simple addition. They combine as vectors at right angles, so F = √(Fₓ² + F_y²). Adding them straight would overstate the force.

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