Kinetic Energy Calculator

Calculate kinetic energy, mass, or velocity. Enter two values to find the third.

Kinetic Energy Formula: KE = ½mv² Where: • KE = kinetic energy (joules, J) • m = mass (kilograms, kg) • v = velocity (meters per second, m/s) Rearrangements: • Mass: m = 2KE/v² • Velocity: v = √(2KE/m)
Example 1 (Energy): A 1500 kg car traveling at 20 m/s (~45 mph) KE = ½ * 1500 * 20² = ½ * 1500 * 400 = 300,000 J = 300 kJ In ft-lb: 300,000 * 0.7376 ~= 221,280 ft-lb Example 2 (Mass): An object has 500 J of kinetic energy at 10 m/s m = (2 * 500) / 10² = 1000 / 100 = 10 kg Example 3 (Velocity): A 0.145 kg baseball has 100 J of kinetic energy v = sqrt(2 * 100 / 0.145) = sqrt(1379.3) ~= 37.1 m/s (~83 mph) Example 4 (Doubling speed): 1000 kg object at 5 m/s: KE = 12,500 J At 10 m/s (double speed): KE = 50,000 J (quadruple energy!)

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It depends on mass and velocity, calculated as KE = ½mv². The faster or heavier an object, the more kinetic energy it has.

Why is velocity squared in the kinetic energy formula?

Velocity is squared because kinetic energy increases exponentially with speed. Doubling velocity quadruples kinetic energy. This comes from the work-energy theorem and integration of force over distance.

What are the units of kinetic energy?

In SI units, kinetic energy is measured in joules (J), where 1 J = 1 kg·m²/s². In imperial units, it's foot-pounds (ft-lb). 1 J ≈ 0.7376 ft-lb.

Can kinetic energy be negative?

No, kinetic energy is always positive or zero. Since velocity is squared in the formula KE = ½mv², the result is always non-negative. Zero kinetic energy means the object is at rest.

What is the difference between kinetic and potential energy?

Kinetic energy is energy of motion (KE = ½mv²), while potential energy is stored energy due to position or configuration (e.g., gravitational PE = mgh). Together they form mechanical energy.

How does kinetic energy relate to momentum?

Both depend on mass and velocity, but differently. Momentum p = mv (linear), while KE = ½mv² (quadratic). They're related by KE = p²/(2m). Momentum is a vector; kinetic energy is a scalar.

What happens to kinetic energy in collisions?

In elastic collisions, kinetic energy is conserved. In inelastic collisions, some kinetic energy converts to heat, sound, or deformation. Momentum is always conserved in isolated systems.

How fast must a car travel to double its kinetic energy?

To double kinetic energy, multiply velocity by √2 ≈ 1.414. For example, if a car at 50 mph has KE = X, it needs ~70.7 mph for KE = 2X. This is why high-speed crashes are so much more severe.

What is rotational kinetic energy?

Rotational KE applies to spinning objects: KE_rot = ½Iω², where I is moment of inertia and ω is angular velocity. Total KE of a rolling object includes both translational (½mv²) and rotational components.

Can you calculate velocity from kinetic energy and mass?

Yes! Rearrange KE = ½mv² to get v = √(2·KE/m). For example, if KE = 100 J and m = 2 kg, then v = √(2·100/2) = √100 = 10 m/s.

What are real-world applications of kinetic energy?

Applications include: vehicle crash analysis (safety design), bullet ballistics, renewable energy (wind turbines convert wind's KE to electricity), sports physics (ball speeds), and roller coaster design.

How does altitude affect kinetic energy?

Altitude doesn't directly affect kinetic energy (KE = ½mv² has no height term), but it affects potential energy. As objects fall, potential energy converts to kinetic energy, increasing velocity and thus KE.