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Kinetic and Potential Energy Calculator

Calculate kinetic energy, gravitational potential energy, total energy, momentum and the landing speed from mass, speed and height.

Enter the values to see the result here.

Formula

Ek=12mv2Ep=mghE=Ek+Epp=mvE_k = \tfrac12 m v^2 \qquad E_p = m g h \qquad E = E_k + E_p \qquad p = m v

If an object is released from height hh with speed vv and no drag acts, it reaches the ground at vf=v2+2ghv_f = \sqrt{v^2 + 2 g h}, because 12mvf2=E\tfrac12 m v_f^2 = E.

Worked example

A 2 kg ball moves at 3 m/s at a height of 10 m above the ground on Earth.

  • Kinetic energy: 12×2×32=9\tfrac12 \times 2 \times 3^2 = 9 J.
  • Potential energy: 2×9.807×10=196.12 \times 9.807 \times 10 = 196.1 J.
  • Total: 205.1205.1 J, and the momentum is 2×3=6 kg m/s2 \times 3 = 6\ \mathrm{kg\,m/s}.
  • Landing speed: 32+2×9.807×10=14.3\sqrt{3^2 + 2 \times 9.807 \times 10} = 14.3 m/s.

Common mistakes

  • Forgetting to square the speed in the kinetic energy.
  • Using grams instead of kilograms. Convert first: 500 g is 0.5 kg.
  • Measuring the height from the wrong reference. Potential energy is relative to the level where you take height to be zero.
  • Mixing up kinetic energy with momentum. Energy is a scalar in joules, momentum is a vector in kg·m/s.

Frequently asked questions

Why does kinetic energy depend on speed squared?

Because the work needed to reach a speed grows with the distance covered, and that distance also grows with speed. The result is that doubling the speed gives four times the energy, which is why high-speed crashes are so much more severe.

What is gravitational potential energy?

It is the energy stored by lifting an object against gravity, mgh, near a planet's surface. It depends on the choice of zero height, so only differences in height matter physically.

What is the unit of energy?

The joule: one newton of force over one metre, or one kilogram metre squared per second squared. A 1 kg book lifted 1 m gains about 9.8 J.

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