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Horizontal component of a force calculator

A-level Forces

Resolving a force into a component along the horizontal when the angle is measured from the horizontal.

F_x = F cos(θ)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

F_xHorizontal component to find 98.3 N

FForce

θAngle to the horizontal

Significant figures

Working

Write the equation
F_x = F cos(θ)
Substitute the values
F_x = 120 × cos(35°)
Calculate
F_x = 98.2982 N
Give the answer to 3 significant figures
F_x = 98.3 N

Worked example

Find Fx, the horizontal component. Given: force F = 120 N; angle to the horizontal θ = 35.0°.

Write the equation
F_x = F cos(θ)
Substitute the values
F_x = 120 × cos(35°)
Calculate
F_x = 98.2982 N
Give the answer to 3 significant figures
F_x = 98.3 N

Symbols and units

Symbol	Quantity	SI unit
F_x	Horizontal component	N
F	Force	N
θ	Angle to the horizontal	°

Horizontal component of a force: rearranged

To find horizontal component: F_x = F cos(θ)
To find force: F = F_x / cos(θ)
To find angle to the horizontal: θ = cos⁻¹(F_x / F)

Exam tip

Check which axis the angle is measured from. If it is from the vertical, cos and sin swap.

Common questions

What is the formula for horizontal component of a force?

The equation is Fx = F cos(θ), where Fx is the horizontal component (N); F is the force (N); θ is the angle to the horizontal (°).

What units should I use for horizontal component of a force?

In SI units: horizontal component in N, force in N, angle to the horizontal in °. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange Fx = F cos(θ)?

Rearranging gives these forms: to find horizontal component: Fx = F cos(θ). to find force: F = Fx / cos(θ). to find angle to the horizontal: θ = cos⁻¹(Fx / F).

Practise horizontal component of a force questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

More forces equations: Newton’s second law, Weight, Moment of a force, Hooke’s law, Pressure, Pressure in a liquid, Density, Vertical component of a force. See the full list on the a-level physics equation calculator page.