Kinetic and Potential Energy Calculator
Finds the kinetic energy of any moving object from its mass and speed. Use it in physics homework, engineering analysis, or whenever you need to know how much energy an object carries in motion.
About this calculator
Kinetic energy is the energy an object possesses due to its motion. It depends on two factors: the object's mass and the square of its velocity. The formula is KE = 0.5 × mass × velocity², where KE is measured in joules (J), mass in kilograms (kg), and velocity in metres per second (m/s). Because velocity is squared, doubling an object's speed quadruples its kinetic energy — a critical insight for safety engineering and collision analysis. The formula derives from the work-energy theorem: the net work done on an object equals the change in its kinetic energy. This makes the calculator useful for everything from analysing car crashes to calculating the energy of a thrown ball.
How to use
Suppose a 1,200 kg car is travelling at 20 m/s. Enter mass = 1200 kg and velocity = 20 m/s. The calculator computes: KE = 0.5 × 1200 × (20²) = 0.5 × 1200 × 400 = 240,000 J, or 240 kJ. This means the car carries 240,000 joules of kinetic energy — equivalent to the energy needed to bring it to a complete stop. Increasing speed to 40 m/s would quadruple KE to 960 kJ, illustrating why speed limits matter.
Frequently asked questions
What is the formula for kinetic energy and how is it derived?
The kinetic energy formula is KE = 0.5 × mass × velocity². It is derived from the work-energy theorem, which states that the work done on an object equals its change in kinetic energy. Integrating the equation of motion (F = ma) over displacement yields the ½mv² expression. The factor of one-half arises naturally from that integration process.
How does doubling velocity affect kinetic energy?
Doubling an object's velocity increases its kinetic energy by a factor of four, because velocity is squared in the formula KE = 0.5 × m × v². This non-linear relationship has major practical implications — for example, a car travelling at 60 mph has four times the kinetic energy of the same car at 30 mph. This is why high-speed collisions are dramatically more destructive than low-speed ones. It also explains why reducing speed limits saves lives disproportionately.
What units does the kinetic energy calculator use and how do I convert them?
This calculator uses SI units: mass in kilograms (kg), velocity in metres per second (m/s), and outputs energy in joules (J). If your speed is in km/h, divide by 3.6 to convert to m/s before entering it. If your mass is in grams, divide by 1,000 to get kilograms. One kilojoule (kJ) equals 1,000 joules, and one megajoule (MJ) equals 1,000,000 joules, which are common units for larger-scale engineering problems.