EngineeringFormulaEngineering Mechanics
Kinetic Energy Calculator
Solve for kinetic energy, mass, or velocity using the classical relation KE = 1/2 m v².
Kinetic energy is the energy an object has because it is moving. In classical mechanics, it depends on two things: mass and speed. Enter any two of the three quantities below to solve for the third using KE = 1/2 m v². This calculator is for non-relativistic motion, where the object's speed is much lower than the speed of light.
m · Mass of the moving object.
v · Speed magnitude of the moving object.
Solution
Enter the required values to calculate kinetic energy.
KE = 1/2 m v²
Formula Sheet
- KEKinetic Energy
- mMass
- vVelocity
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| KE | Kinetic Energy | Energy associated with an object's translational motion. | J, kJ, MJ, ft·lbf |
| m | Mass | Mass of the moving object. | g, kg, lb |
| v | Velocity | Speed magnitude of the moving object. | m/s, km/h, mph, ft/s |
How to Use This Calculator
- 01Choose which quantity to solve for - Kinetic Energy, Mass, or Velocity - using the solve-for selector.
- 02Enter the other two known values and pick the correct unit for each field.
- 03Select Calculate to see the result in base SI units, plus a secondary conversion where it's useful.
- 04Use the worked examples and variable table below if you want to check the setup by hand or sanity-check whether your result is in a realistic range.
How the Formula Works
Classical translational kinetic energy is defined as one-half the mass multiplied by the square of the speed: KE = 1/2 m v². Because velocity is squared, speed has a much stronger effect on kinetic energy than mass does - doubling the mass doubles KE, but doubling the speed multiplies KE by four.
That squared-speed relationship is why high-speed impacts become much more severe so quickly. It's also why kinetic energy is commonly used in mechanics, transportation, and safety calculations to compare moving systems with different masses and speeds. This calculator treats velocity as a speed magnitude, so direction is not considered.
Worked Example 01
Calculating the kinetic energy of a moving car
Known
- Mass (m): 1,500 kg
- Velocity (v): 20 m/s
Formula
KE = 1/2 m v²
Substitution
KE = 1/2 × 1,500 × 20²
Result
KE = 300,000 J (300 kJ)
A 1,500 kg car traveling at 20 m/s stores 300 kJ of kinetic energy.
Worked Example 02
Solving for mass from energy and speed
Known
- Kinetic Energy (KE): 120 J
- Velocity (v): 10 m/s
Formula
m = 2 KE / v²
Substitution
m = (2 × 120) / 10²
Result
m = 2.4 kg
If an object has 120 J of kinetic energy while moving at 10 m/s, its mass is 2.4 kg.
Worked Example 03
Solving for velocity from energy and mass
Known
- Kinetic Energy (KE): 250 J
- Mass (m): 2 kg
Formula
v = √(2 KE / m)
Substitution
v = √((2 × 250) / 2)
Result
v ≈ 15.81 m/s
A 2 kg object must travel at about 15.81 m/s to have 250 J of kinetic energy.
Applications
- 01Estimating impact severity for vehicles, tools, and moving equipment
- 02Checking textbook and laboratory mechanics problems
- 03Comparing how changes in mass or speed affect motion energy
Assumptions
- 01The motion is classical (non-relativistic), so KE = 1/2 m v² is valid.
- 02Velocity is treated as a speed magnitude only; direction is not modeled.
- 03The object is represented as a single moving mass with translational motion.
Where This Model Stops
- 01Not valid for speeds approaching the speed of light - relativistic kinetic energy requires a different expression.
- 02Does not include rotational kinetic energy, deformation losses, drag, or any change in energy over time.
References
- [1]7.2 Kinetic Energy - University Physics Volume 1
OpenStax
Defines classical kinetic energy as KE = 1/2 m v² and explains its SI units.
- [2]Conservation of Energy
NASA Glenn Research Center
Uses K = (m u²) / 2 and the specific kinetic energy form k = u² / 2 in an engineering context.
Frequently Asked Questions
Why does speed affect kinetic energy more than mass?
Because speed is squared in KE = 1/2 m v². Doubling mass only doubles kinetic energy, but doubling speed increases kinetic energy by a factor of four.
Can I use this for cars, projectiles, or machinery?
Yes - as long as you know the mass and speed, the same classical equation applies. The calculator returns translational kinetic energy only; application-specific decisions may still require other checks such as momentum, drag, or material limits.
Why doesn't direction matter here?
Kinetic energy depends on speed magnitude, not direction. Enter the object's speed as a positive value; motion in opposite directions has the same kinetic energy at the same speed.
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