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Kinetic Energy Calculator: Calculate Kinetic Energy from Mass and Velocity

Compute kinetic energy from mass and velocity using KE = ½mv²

PhysicsBy Numora physics teamReviewed by Numora engineering review team, Ph.D. in PhysicsUpdated 

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Assumptions
kg
m/s
Kinetic energy
675.000

Translational energy only

An object of mass 1500kg moving at 30m/s has kinetic energy 675.000.

Substantial — kJ range
In kilojoules675
In kilocalories161,3289
In kilowatt-hours0,1875
In foot-pounds497.854,35
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⚡ The answer

Kinetic energy is the energy an object has due to its motion. It equals one half the mass times velocity squared: KE = ½mv². Because velocity is squared, doubling the speed quadruples the kinetic energy — the most important practical implication of the formula. Measured in joules in SI units.

Quick takeaway

Quickly calculate kinetic energy (KE) from an object's mass and velocity using the fundamental physics formula KE = ½mv². This calculator provides instant results in joules, along with practical conversions to kilojoules, kilocalories, kilowatt-hours, and foot-pounds, making complex physics accessible for everyday applications. A key insight revealed is the quadratic relationship between velocity and kinetic energy: doubling an object's speed quadruples its kinetic energy, a crucial principle for understanding vehicle safety, collision impacts, and energy transformations in various physical systems. Use this tool to explore how different masses and speeds affect energy, from a moving car to a high-speed bullet.

What is a kinetic energy?

Use this kinetic energy calculator to compute the energy of a moving object using the standard mechanics formula KE = ½mv². Enter mass in kilograms and velocity in meters per second; the calculator returns kinetic energy in joules with conversions to kilojoules, kilocalories, kilowatt-hours, and foot-pounds. This tool is built against the OpenStax University Physics curriculum and the Système International (SI) joule definition, ensuring accuracy for physics, engineering, and safety calculations. It helps visualize the impact of mass and velocity on an object's energy, highlighting the critical role of the velocity-squared term in real-world applications like vehicle safety and collision analysis. Gain practical insight into energy transformations and conservation principles.

The formula

KE = ½ × m × v²
  • KE — kinetic energy in joules (J)
  • m — mass in kilograms (kg)
  • v — velocity in meters per second (m/s)

Source: Classical Newtonian mechanics — work-energy theorem.

Worked examples

1Highway-speed car

Inputs
mass: 1500velocity: 30
Walkthrough

A 1,500 kg car at 30 m/s (108 km/h, 67 mph) has KE = ½ × 1,500 × 30² = 675,000 J = 675 kJ. That's about 161 kcal — the same energy as roughly 2 large bananas, but compressed into a kinetic state that brakes must dissipate as heat to stop the vehicle.

2Why doubling speed quadruples energy

Inputs
mass: 1500velocity: 60
Walkthrough

Same 1,500 kg car at 60 m/s. KE = ½ × 1,500 × 60² = 2,700,000 J = 2,700 kJ. Compared to 30 m/s (675 kJ), the energy is exactly 4× higher. This is why doubling driving speed roughly quadruples both braking distance and crash severity.

3Bullet — small mass, very high velocity

Inputs
mass: 0.005velocity: 400
Walkthrough

A 5-gram (0.005 kg) rifle bullet at 400 m/s has KE = ½ × 0.005 × 400² = 400 J. Compared to a 70 kg human walking at 1.5 m/s (KE ≈ 79 J), the bullet carries 5× more energy in a tiny mass — concentrated, hence destructive.

How to use this calculator

  1. Mass — Mass of the object in kilograms. 1 kg = 2.205 lb.
  2. Velocity — Speed of the object in m/s. 30 m/s ≈ 67 mph ≈ 108 km/h.
  3. Read the result. Use the worked examples below to sanity-check against a known scenario.

Kinetic energy at different speeds (1500 kg car)

Speed (mph)Speed (m/s)KE (kJ)Stopping distance
208.9460~6 m
3013.41135~13 m
6026.82540~52 m
8035.76959~92 m

Stopping distance scales with KE / friction force, hence roughly with v².

Frequently asked questions

What is kinetic energy?
The energy an object has because it's moving. Defined as KE = ½mv², where m is mass and v is velocity. Measured in joules in SI units.
Why does the formula have a factor of ½?
It comes from integrating force over distance to compute work. For a force F = ma starting from rest, the work done after time t is F · d = ma · ½at² = ½m(at)² = ½mv².
Why is velocity squared instead of just v?
Because energy comes from the work-energy theorem, which integrates F = ma over distance. The result is proportional to v². The squared term is why doubling driving speed quadruples crash severity.
What's the difference between kinetic energy and momentum?
Momentum is p = mv (linear in velocity). Kinetic energy is KE = ½mv² (quadratic in velocity). Both are conserved in elastic collisions, but only momentum is conserved in inelastic collisions where some KE becomes heat.
How do I convert joules to calories?
Divide joules by 4,184 to get food calories (kilocalories). 1 kJ = 0.239 kcal. So 675,000 J of car kinetic energy ≈ 161 kcal.
Does the direction of velocity matter for KE?
No. Kinetic energy is a scalar quantity — it depends only on the speed (magnitude of velocity), not direction. v² is the same regardless of direction.
Where does kinetic energy go when something stops?
It converts to other forms — typically heat (in brakes, tires, road), sound, and material deformation. Total energy is conserved by the first law of thermodynamics.
How does KE compare for a small fast object vs a large slow one?
Use KE = ½mv². A 5g bullet at 400 m/s has 400 J; a 70 kg person walking at 1.5 m/s has 79 J. Small mass + high velocity beats large mass + low velocity in KE.

Kinetic Energy glossary

Kinetic energy
Energy an object has due to its motion. Equal to ½mv² in classical mechanics.
Joule (J)
SI unit of energy. One joule is the work done by a force of one newton over a distance of one meter.
Kilojoule (kJ)
1,000 joules. Used for everyday energy quantities — a Calorie (food calorie) is 4,184 J = 4.184 kJ.
Velocity
Speed in a given direction. In KE = ½mv², only the magnitude (speed) matters because v² is direction-independent.
Work-energy theorem
The total work done on an object equals its change in kinetic energy. Underpins the derivation of KE = ½mv².
Conservation of energy
Energy can change form (KE → heat, KE → potential, etc.) but cannot be created or destroyed in an isolated system.

How we built this calculator

Methodology

Kinetic energy is the energy stored in motion. The formula KE = ½mv² comes from integrating Newton's second law over distance: starting from rest, the work done by a constant force F over distance d is F·d, and using F = ma and d = ½at², the kinetic energy reached at the end works out to ½mv².

This calculator was written by Numora physics team and reviewed by Numora engineering review team, Ph.D. in Physics before publication. Both names link to full bios with verifiable credentials.

Formula source
Classical Newtonian mechanics — work-energy theorem
Last reviewed
2026-04-29
Reviewer
Numora engineering review team, Ph.D. in Physics
Calculation runs
Client-side only
NP
WRITTEN BY
Numora physics team
NE
REVIEWED AND APPROVED BY
Numora engineering review team, Ph.D. in Physics
In this review:
  • Verified the formula matches Classical Newtonian mechanics — work-energy theorem (Standard Système International (SI) units).
  • Confirmed the rounding rule applied by the engine: energy to 2 decimal places in joules.
  • Recomputed all 3 worked examples by hand and confirmed the results match the engine.
  • Confirmed all 5 cited sources resolve to current pages on the issuing institution.
  • Cross-checked the 4-row comparison table for arithmetic consistency at the baseline scenario.

Reviewed on 2026-04-29 · Next review: 2027-04-29

See editorial policy

Sources & references

Every numeric assumption traces to a primary source.

  1. OpenStax University Physics, Volume 1 — Chapter 7 Work and Kinetic EnergyUSA
  2. MIT OpenCourseWare 8.01 — Classical Mechanics, Energy lecturesUSA
  3. NIST Reference on Constants, Units, and Uncertainty — joule definitionUSA
  4. Halliday, Resnick & Walker, Fundamentals of Physics (10th ed.)INT
  5. BIPM SI Brochure (2019)INT
  6. Numora Editorial Policy. numora.net/editorial-policy