Calculator Suite

Kinetic Energy Calculator

Calculate kinetic energy, mass, or velocity using KE = ½mv²

Kinetic Energy Problem Setup

Use KE = ½mv² to solve for kinetic energy, mass, or velocity

Common Scenarios

Car Kinetic Energy

Energy of a car traveling at highway speed

Bullet Energy

High velocity, low mass example

Cyclist Speed

What speed for a given energy output?

Energy References

Walking: ~3J/kgRunning: ~50J/kgCar (city): ~200kJCar (highway): ~500kJ

Kinetic Energy Formula

Energy of motion - fundamental energy equation

The Equation

KE = \frac{1}{2}mv^2

$KE$ = Kinetic energy (in Joules or foot-pounds)

$m$ = Mass (in kilograms or pounds-mass)

$v$ = Velocity (in m/s or ft/s)

Energy Concepts

Energy: The capacity to do work or cause change

Kinetic: Energy due to motion (moving objects)

Conservation: Energy cannot be created or destroyed

Transfer: Kinetic energy can convert to potential energy and vice versa

Velocity-Squared Effect

Kinetic energy scales with the square of velocity:

2× speed = 4× energy

3× speed = 9× energy

This explains why high-speed impacts are so destructive.

Real-World Applications

Vehicle Safety: Crash test energy analysis

Sports: Impact forces in athletics

Engineering: Machine design and energy storage

Ballistics: Projectile impact analysis

Space: Orbital mechanics and spacecraft

Understanding Kinetic Energy

TL;DR

Kinetic Energy is the energy an object has because it is moving. It depends heavily on speed—doubling your speed quadruples your energy ( $v^2$ ).

The Energy of Motion

Any object with mass that is moving has Kinetic Energy. To stop the object, you must do work against it equal to its kinetic energy.

The $\frac{1}{2}$ factor comes from calculus (integrating $F=ma$ over distance), and the $v^2$ shows that speed is the most critical factor.

How to Use This Calculator

Select Goal: Do you want to find Energy, Mass, or Speed?
Choose System: SI (Joules/kg/m/s) or Imperial (ft-lb/lbs/ft/s).
Input Data: Enter the two values you know.
Get Results: View the calculated energy and the energy curve.

Real-World Example: Highway Speeds

Scenario:

A 1500 kg car accelerates from 50 km/h (13.9 m/s) to 100 km/h (27.8 m/s). How does the energy change?

Analysis:

At 50 km/h: $0.5 \times 1500 \times 13.9^2 \approx 145,000\text{ J}$
At 100 km/h: $0.5 \times 1500 \times 27.8^2 \approx 580,000\text{ J}$
Conclusion: Doubling speed quadruples the energy (and danger)!

3 Key Checks (The "SOP")

Always Positive

Mass is + and $v^2$ is +. KE can never be negative.

Zero Speed

If velocity is 0, KE is exactly 0. Stationary objects have no kinetic energy.

Square Root

Solving for $v$ ? You must take the root of ( $2KE/m$ ).

Assumptions & Limitations

Classical Limit: This formula ( $\frac{1}{2}mv^2$ ) is inaccurate near the speed of light (Relativity takes over).
Rigid Bodies: Assumes energy is not lost to internal heat/deformation during motion itself.
Point Mass: Treats the object as a single point for simple calculation.

Video Tutorials

Frequently Asked Questions

Can Kinetic Energy be negative?

No. Mass is always positive, and velocity squared ( $v^2$ ) is always positive. Therefore, KE must be zero or positive.

Where does the 1/2 come from?

It comes from the calculus of motion. When you integrate force over distance ( $\int F dx$ ), the result for constant mass involves a $\frac{1}{2}$ factor.

Is higher mass or higher speed better for energy?

Speed wins! Because velocity is squared, a small increase in speed gives a huge boost in energy compared to the same increase in mass.

Related Physics Tools

Linear Motion Calculator Velocity² Calculator Force Calculator Displacement Calculator