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Force, velocity and power: an interactive explainer

Power is force times velocity, so the strongest person is not automatically the most powerful.

Little BuffPublished Updated

Strength tests ask how much force you can produce; sport asks how much, how fast. The quantity that joins them is power = force x velocity, and a muscle cannot give you both at once.

Power is an area

05001000150020000246810Velocity (m/s)Force (N)Area = power
Width is velocity, height is force, and the area of the rectangle is power. Drag the sliders.
  • 2,000 Wpower = force x velocity

Example arithmetic, not a measurement. Do not multiply a peak force by a peak velocity from different instants; published punch figures report peak force and peak hand speed separately.

Why more force does not mean more power

Force falls as shortening speed rises (a hyperbolic relationship). Power is zero at rest, zero at top speed and highest in between: in this schematic curve, at about 31% of maximum speed. The shape parameter is illustrative, not a measured value.

050%100%0%25%50%75%100%Shortening speed (% of the muscle's maximum)ForcePowerPeak power at about 31% of maximum speed in this schematic
Schematic force-velocity and power curves. Force and power are each shown as a share of their own maximum. The shape of the curve is textbook-style; the parameter is illustrative.
  • 32%of maximum force still available
  • 100%of peak power

Maximal power is limited by the force-velocity and length-tension relationships, and fibre-type makeup is one morphological factor. In the first 50-75 milliseconds, how fast force rises is set mainly by voluntary activation and motor-unit firing rate, which heavy and explosive training can both improve. In one study of 15 men, 14 weeks of heavy training raised quadriceps force by 16% and force at 30 ms by 26%, with higher neural drive. It is one small study of one muscle group, and rate of force development is hard to measure reliably.

Sources: Cormie 2011, Samozino 2008, Maffiuletti 2016, Aagaard 2002

An analogy: torque and horsepower, and where it breaks

Editorial analogy, not a sourced finding. An engine's torque is its pulling force at the crankshaft; horsepower is torque times engine speed. Likewise a muscle gives most force when slow and most power at a middle speed.

It breaks in three places: a muscle has no gearbox to trade force for speed, tendons store and return energy, and neural activation limits how fast force can rise in the first 50-75 ms. So someone far stronger in a slow test is not necessarily more powerful at sport speeds; in the combat route, punch force tracked lower-body force rather than upper-body strength.

Sources: Cormie 2011, Samozino 2008, Maffiuletti 2016

Sources

  1. Cormie et al. 2011: Developing maximal neuromuscular power: Part 1--biological… accessed
  2. Samozino et al. 2008: A simple method for measuring force, velocity and power… accessed
  3. Maffiuletti et al. 2016: Rate of force development: physiological and… accessed
  4. Aagaard et al. 2002: Increased rate of force development and neural drive of… accessed

Not medical advice. Published research, summarised for general information. Speak to a doctor or qualified coach before changing training, food or weight.

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Topics: Fitness journeysStrengthScience