PhysicsCalcs
Work, Energy & Power

Force to Power Calculator

Calculate power from force and velocity using P = Fv or P = Fv cos(\u03B8). Solve for force, velocity, or compute average power from work and time with unit conversions and formula steps.

Interactive calculator

Force to Power Calculator

Calculate power from force and velocity using P = Fv or P = Fv cos(\u03B8). Solve for force, velocity, or power from work and time.

Try an example

Force applied

Speed of the object

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: P = Fv, P = Fv cos\u03B8, find force, find velocity, or P = W/t.
  • Enter known values with units.
  • Click Calculate for result and formula steps.

Table of Contents

Key Takeaways

  • P = Fv: power equals force times velocity (when aligned).
  • P = Fv cos(θ): general case with an angle between force and velocity.
  • F = P / v: at a given speed, more power means more force (or vice versa).
  • P = W / t: average power equals work divided by time.
  • Power is measured in watts (W). 1 W = 1 J/s = 1 N·m/s.
  • 1 mechanical hp ≈ 745.7 W.

What Is Force to Power?

Force to power describes the relationship between force, velocity, and power. When a force moves an object at a steady velocity, the power delivered is P = Fv. This is a direct consequence of P = W/t and W = Fd.

P = Fv (Force Parallel to Velocity)

P=FvP = Fv

When force is in the same direction as velocity, power equals force times speed. Force in newtons, velocity in m/s gives power in watts.

P = Fv cos(\u03B8) (General Case)

P=Fvcos(θ)P = Fv cos(θ)

When force is at angle θ to velocity, only the component along the velocity contributes to power. At 90°, no power is delivered.

P = W / t (Average Power)

P=W/tP = W / t

Average power equals total work (or energy) divided by time. This is the most general definition of power.

Power Units

UnitTo Watts
1 kW1 000 W
1 MW1 000 000 W
1 hp (mechanical)≈ 745.7 W
1 PS (metric)≈ 735.5 W
1 ft·lbf/s≈ 1.356 W

How to Use the Calculator

  1. Choose a calculation mode.
  2. Enter known values with units.
  3. Click Calculate.
  4. Review the result, formula steps, and interpretation.

Example Calculations

500 N at 20 m/s

P = 500 × 20 = 10 000 W = 10 kW

1000 N, 10 m/s, 30°

P = 1000 × 10 × cos(30°) ≈ 8 660 W

50 kW at 100 km/h → force

F = 50000 / 27.78 ≈ 1 800 N

1 MJ in 10 min

P = 1 000 000 / 600 ≈ 1 667 W

Common Mistakes

  • Using km/h without converting to m/s.
  • Confusing horsepower types (mechanical vs metric vs electrical).
  • Forgetting to use the cos(\u03B8) component when force is not parallel.
  • Treating instantaneous power as if it were average power.
  • Mixing N with kN without converting.

Accuracy and Limitations

P = Fv gives instantaneous power when force and velocity are constant and aligned. For time-varying forces or speeds, integration is needed. This calculator does not include mechanical losses (friction, drag, drivetrain). The angle mode assumes constant angle. This tool is educational.

FAQ

How do you convert force to power?›

Power = force × velocity. P = Fv when force is in the direction of motion.

Why is velocity needed?›

Power measures energy transfer rate. A force does no work (and delivers no power) without movement.

What if force is at an angle?›

Use P = Fv cos(θ), where θ is the angle between the force vector and the velocity vector.

Can P = Fv give negative power?›

Yes. When force opposes velocity (braking), power is negative — energy is being absorbed.

What is the relationship between P, W, and t?›

P = W/t. Average power equals total work (energy) divided by total time.

How do I find the force needed at a given speed and power?›

F = P / v. For example, at 100 km/h with 50 kW of engine power, F = 50000 / 27.78 ≈ 1800 N.

What units should I use?›

Any units work — the calculator converts automatically. SI: N, m/s, W.

Sources

  1. OpenStax University Physics – Power
  2. NIST SI Units
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish