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Vertical component of a force calculator

A-level Forces

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

Fy = F sin(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

68.8 N

Working

  1. Write the equation
    Fy = F sin(θ)
  2. Substitute the values
    Fy = 120 × sin(35°)
  3. Calculate
    Fy = 68.8292 N
  4. Give the answer to 3 significant figures
    Fy = 68.8 N

Worked example

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

  1. Write the equation
    Fy = F sin(θ)
  2. Substitute the values
    Fy = 120 × sin(35°)
  3. Calculate
    Fy = 68.8292 N
  4. Give the answer to 3 significant figures
    Fy = 68.8 N

Symbols and units

SymbolQuantitySI unit
FyVertical componentN
FForceN
θAngle to the horizontal°

Vertical component of a force: rearranged

  • To find vertical component: Fy = F sin(θ)
  • To find force: F = Fy / sin(θ)
  • To find angle to the horizontal: θ = sin−1(Fy / F)

Exam tip

The vertical component is the part of the force that lifts or pushes down. Use it in vertical equilibrium questions.

Common questions

What is the formula for vertical component of a force?

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

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

In SI units: vertical 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 Fy = F sin(θ)?

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

Practise vertical component of a force questions

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

Related

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