Kinetic Energy Calculator
Calculate kinetic energy, mass, velocity, rotational KE, and relativistic KE
KE = ½mv²
Kinetic Energy = ½ × Mass × Velocity²
Kinetic Energy Quick Reference
Linear:
KE = ½mv²
Rotational:
KE = ½Iω²
SI Unit:
Joule (J) = kg·m²/s²
Relativistic:
KE = (γ-1)mc²
Understanding Kinetic Energy
Kinetic energy is the energy possessed by an object due to its motion. Any moving object, from a speeding car to a spinning top, has kinetic energy. This energy depends on both the mass and the velocity of the object.
The Kinetic Energy Formula
The formula for linear (translational) kinetic energy is KE = ½mv², where m is mass and v is velocity. Notice that kinetic energy is proportional to the square of velocity - doubling the speed quadruples the kinetic energy.
Rotational Kinetic Energy
For rotating objects, kinetic energy is calculated as KE = ½Iω², where I is the moment of inertia and ω (omega) is the angular velocity. The moment of inertia depends on how mass is distributed around the axis of rotation.
Relativistic Kinetic Energy
At speeds approaching the speed of light, the classical formula breaks down. Einstein's relativistic formula is KE = (γ - 1)mc², where γ (gamma) is the Lorentz factor: γ = 1/√(1 - v²/c²). This formula reduces to the classical formula at low speeds.
Work-Energy Theorem
The work-energy theorem states that the work done on an object equals the change in its kinetic energy: W = ΔKE. This fundamental principle connects force, displacement, and energy.
Examples of Kinetic Energy
- Baseball: ~120 J at 40 m/s
- Running person: ~1,000 J at 5 m/s
- Car at 60 mph: ~340,000 J
- Bullet: ~1,000-2,000 J
Conservation of Energy
Kinetic energy can be transformed into other forms of energy and vice versa. In a closed system, total energy is conserved. For example, a falling object converts gravitational potential energy into kinetic energy.
Worked Example
A 1,500 kg car travels at 25 m/s (about 90 km/h or 56 mph). Its kinetic energy is KE = ½ × 1500 × 25² = ½ × 1500 × 625 = 468,750 J ≈ 469 kJ. If the same car slows to 12.5 m/s, the energy falls to about 117 kJ — a quarter of the original, not half — because energy scales with the square of speed. This is why braking distance grows so quickly with speed and why the calculator also lets you solve backwards for mass (m = 2KE/v²) or velocity (v = √(2KE/m)).
Frequently Asked Questions
How do I calculate kinetic energy from mass and velocity?+
Use KE = ½mv² with mass in kilograms and velocity in meters per second; the result is in joules. For example, a 0.145 kg baseball thrown at 40 m/s carries ½ × 0.145 × 1600 = 116 J. The calculator also converts common units, so you can enter grams or km/h without converting by hand.
Can this tool solve for mass or velocity instead of energy?+
Yes. Besides computing KE, it rearranges the formula to find mass (m = 2KE / v²) or velocity (v = √(2KE / m)) from the other two values. This is useful for problems like finding how fast an object must move to carry a specified energy.
What is rotational kinetic energy and when do I need it?+
A spinning object stores energy given by KE = ½Iω², where I is the moment of inertia in kg·m² and ω is angular velocity in radians per second. Use the rotational mode for flywheels, wheels, turbines, or any rigid body rotating about an axis; a rolling object has both translational and rotational kinetic energy.
When should I use the relativistic kinetic energy mode?+
The classical ½mv² formula is accurate at everyday speeds but underestimates energy as speed approaches the speed of light. The relativistic mode uses KE = (γ − 1)mc², which matters above roughly 10% of light speed (about 30,000 km/s) — relevant for particle physics, not for cars or projectiles.
Is the kinetic energy calculator free and mobile-friendly?+
Yes. It is free, requires no sign-up, and every calculation runs directly in your browser with nothing sent to a server. It works on phones and tablets, making it convenient for physics homework or lab work on any device.
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