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Physics

Kinetic Energy

KE = ½mv². Free online Kinetic Energy. Calculate kinetic energy online — fast, accurate, mobile-friendly, no signup needed.

KE = ½·m·v².
KE (J)
200,000

Derivation

  1. ├── 01Givenm = 1000, v = 20
  2. ├── 02Formula{let t=e.m,a=e.v;return.5 × t × a²}
  3. ├── 03Substitute{let t=e.1000,a=e.20;return.5 × t × a²}
  4. └── 04Compute KE (J)200,000
Did you know?

The phrase "kinetic energy" was coined by William Thomson (Lord Kelvin) and Peter Guthrie Tait in 1867 — before that physicists called it vis viva, "living force".

§01What is

Understanding the Kinetic Energy

The Kinetic Energy computes KE (J) from 2 inputs: mass (kg), velocity (m/s). KE = ½mv².

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Kinetic Energy sits in that toolkit — it KE = ½mv². Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

{let t=e.m,a=e.v;return.5 × t × a²}

Where

m
Mass (kg)
v
Velocity (m/s)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Mass (kg) = 1000, Velocity (m/s) = 20.

  1. 01Start by noting the input — Mass (kg): 1000.
  2. 02Start by noting the input — Velocity (m/s): 20.
  3. 03Substitute these values into the formula: {let t=e.m,a=e.v;return.5 × t × a²}
  4. 04Compute KE (J): the calculator returns 200000.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Kinetic Energy Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Mass (kg) halved

m = 500 (from 1000)

Keep every other input at its default and halve the mass (kg). See how ke (j) responds.

  1. 01New Mass (kg): 500
  2. 02Baseline KE (J): 200000
  3. 03New KE (J): 100000
  4. 04KE (J) decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Mass (kg) doubled

m = 2000 (from 1000)

Keep every other input at its default and double the mass (kg). See how ke (j) responds.

  1. 01New Mass (kg): 2000
  2. 02Baseline KE (J): 200000
  3. 03New KE (J): 400000
  4. 04KE (J) increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Velocity (m/s) halved

v = 10 (from 20)

Keep every other input at its default and halve the velocity (m/s). See how ke (j) responds.

  1. 01New Velocity (m/s): 10
  2. 02Baseline KE (J): 200000
  3. 03New KE (J): 50000
  4. 04KE (J) decreases by 75% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Velocity (m/s) doubled

v = 40 (from 20)

Keep every other input at its default and double the velocity (m/s). See how ke (j) responds.

  1. 01New Velocity (m/s): 40
  2. 02Baseline KE (J): 200000
  3. 03New KE (J): 800000
  4. 04KE (J) increases by 300% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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