Kinetic Energy Calculator

Kinetic energy is calculated with the formula KE = ½mv², where m is the mass of the object in kilograms and v is its velocity in meters per second. The result is expressed in joules (J). For example, an object with a mass of 2 kg moving at 10 m/s has a kinetic energy of ½ × 2 × 10² = 100 joules. Because velocity is squared, kinetic energy grows much faster than mass does — doubling the speed of an object quadruples its kinetic energy, while doubling the mass only doubles it.

You can rearrange the kinetic energy formula to isolate either variable. To solve for mass: m = 2·KE / v². To solve for velocity: v = √(2·KE / m). For instance, if an object has 100 J of kinetic energy and a mass of 2 kg, its velocity is √(2 × 100 / 2) = √100 = 10 m/s. This calculator lets you toggle which variable you're solving for and automatically rearranges the formula for you.

In the standard SI system, kinetic energy is measured in joules (J), where 1 joule equals 1 kilogram·meter²/second² (kg·m²/s²). Mass should be entered in kilograms (kg) and velocity in meters per second (m/s) to get a result directly in joules. If you have mass in grams or velocity in km/h, convert them to kilograms and meters per second first, or the resulting energy value will be off by a scaling factor.

Kinetic energy depends on velocity squared because energy is derived from the work needed to accelerate an object from rest, and that work integrates force over distance while the object is speeding up. Mathematically, this integration produces a v² term rather than a linear v term. The practical consequence is dramatic: a car moving at 60 mph carries four times the kinetic energy of the same car at 30 mph, not just twice as much — which is why small increases in speed cause outsized increases in stopping distance and crash severity.

The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE = KE_final − KE_initial. This means that whenever a force accelerates or decelerates an object, the work that force performs is exactly stored in or removed from the object's kinetic energy. For example, braking a car does negative work on it, removing kinetic energy until the car stops, while a falling object gains kinetic energy as gravity does positive work on it.

No, kinetic energy can never be negative, since it depends on velocity squared (v²) and mass is always positive — squaring removes any sign from the velocity. This also means direction doesn't matter for the kinetic energy value itself: an object moving left at 10 m/s has exactly the same kinetic energy as one moving right at 10 m/s. Kinetic energy is a scalar quantity, unlike momentum or velocity, which are vectors and do depend on direction.