Kinetic energy calculator
Kinetic energy, speed or mass from E = ½mv².
Fill in the fields and the result will appear here automatically.
Find translational kinetic energy, speed from energy, or mass from energy and speed. Compare speeds in the same reference frame: kinetic energy depends on motion relative to an observer. The ½mv² formula is classical; rotation, collision deformation and relativistic effects are excluded. Energy alone does not determine braking distance.
How it works
Formula and logic
E = m v²/2; v = √(2E/m); m = 2E/v². Direct calculation requires positive mass; speed and energy are nonnegative. The inverse returns speed magnitude, not direction. Doubling speed at fixed mass quadruples energy.
Example
2 kg at 3 m/s gives E = 2 × 3²/2 = 9 J. At 6 m/s the same body has 36 J. Conversely, E = 100 J and m = 8 kg give √25 = 5 m/s; E = 50 J and v = 10 m/s give m = 1 kg.
Fields and units
- What to find — list option
- Mass — kg
- Speed — m/s
- Energy — J
- Mass — kg
- Energy — J
- Speed — m/s
How to use
- — Choose the unknown and enter the other two quantities in kg, m/s and J.
- — Enter speed magnitude. Convert km/h to m/s by dividing by 3.6: 36 km/h = 10 m/s.
- — Zero speed is valid for energy. It cannot determine mass: this inverse formula would require division by zero.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: classical kinetic energy and reference frame
- Limitation
- Classical translational kinetic energy. Speeds comparable to the speed of light require a relativistic calculation.
FAQ
Can speed be negative?
The input is speed magnitude. Opposite velocities +v and −v have the same energy because the formula squares the value.
Is this the total energy of a wheel?
No. Its translational part is mv²/2; rotational energy adds Iω²/2. Moment of inertia is not an input here.
Can I obtain braking distance or impact force?
No. Braking distance needs braking forces and conditions; average impact force needs a stopping distance or time and a collision model.
How should energy given in kilojoules be entered?
The field uses joules: 1 kJ = 1000 J. For 1 kJ and a mass of 80 kg, enter 1000 and 80: v = √(2000/80) = 5 m/s. Entering 1 instead of 1000 changes the calculation, not just the label.