Kinetic Energy Calculator: E = 1/2 mv^2

The energy of motion: kinetic energy, mass or speed.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • E_k = \tfrac12\,m\,v^2
  • v = \sqrt{\frac{2E_k}{m}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the kinetic energy: kinetic energy = 1/2 x mass x speed^2
  2. Put the values in (every value in its SI unit): kinetic energy = 1/2 x 1200 x 25^2
  3. The answer: kinetic energy: 375000 J
  4. The same answer in other units: 375 kJ; 0.104167 kWh; 276586 ft lbf

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Speed; Kinetic energy (leave it as it is if this is what you are finding) 375000 J; Mass (leave it as it is if this is what you are finding) 1200 kg.

  1. The formula, arranged to find the speed: speed = square root of ((2 x kinetic energy) / (mass))
  2. Put the values in (every value in its SI unit): speed = square root of ((2 x 375000) / (1200))
  3. The answer: speed: 25 m/s
  4. The same answer in other units: 90 km/h; 55.9234 mph

Common questions

What is the formula for kinetic energy?

Half the mass times the speed squared. A 1200 kg car at 25 m/s (90 km/h) has 375 000 J.

Why does speed matter more than mass?

Because the speed is squared. Doubling the speed quadruples the energy, but doubling the mass only doubles it.

How do I find the speed from the kinetic energy?

Square root of twice the energy divided by the mass.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (kinetic energy).

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