Ohm's Law Calculator (V = I × R)
Calculate voltage, current or resistance using Ohm's Law (V=I×R). The calculator also computes electric power. Fast, free and no registration required.
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Kinetic Energy Calculator (Ek = ½mv²)
Kinetic energy is one of the fundamental quantities in physics that describes motion. Every moving object — a car, a ball, a runner, a bullet — possesses kinetic energy that depends on its mass and velocity. The formula for kinetic energy is Ek = ½ · m · v², where m is the mass in kilograms and v is the velocity in metres per second. The result is expressed in joules (J), the standard SI unit of energy. Our kinetic energy calculator lets you compute the kinetic energy of any object instantly. Simply enter the object mass (in kg) and its velocity (in m/s). The calculator automatically converts the result to kilojoules (kJ) and kilocalories (kcal), and also displays the velocity in km/h and the momentum of the body. Applications are numerous: road safety analysis, sports science, physics lessons, safety system design. Understanding kinetic energy is crucial when analysing accidents — a car travelling at 100 km/h has four times more kinetic energy than the same car at 50 km/h, which explains why speed so dramatically affects collision outcomes. The calculator helps you grasp these relationships in a practical, intuitive way. The classic Newtonian formula is accurate for everyday speeds. At velocities below 10% of the speed of light (approximately 30 000 km/s), the relativistic correction is below 1% and can safely be ignored for engineering and educational purposes.
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How we calculate kinetic energy
The calculator uses the classical (non-relativistic) mechanics formula: Ek = ½ · m · v², where m is the mass in kg and v is the velocity in m/s. The result in joules (J) is divided by 1 000 to obtain kilojoules (kJ), and by 4 184 to obtain kilocalories (kcal) — the conversion factor important in thermodynamics and nutrition science. Momentum is calculated as p = m · v (kg·m/s). It is a vector quantity important for collision analysis and systems of bodies — unlike energy, momentum grows linearly with velocity, not quadratically. Velocity in km/h is derived as v_kmh = v_ms × 3.6, which follows from the definition of units (1 m/s = 3 600 m/h = 3.6 km/h). The calculator takes velocity in m/s as input (the physics standard) and automatically shows the equivalent value in km/h for intuitive interpretation of results.
Example: a runner and a motorway car
Example 1 — runner: A person weighing 70 kg running at 10 m/s (36 km/h, sprint pace) has kinetic energy Ek = ½ × 70 × 10² = 3 500 J = 3.5 kJ. That is the same energy as lifting 357 kg by one metre. Example 2 — passenger car: A car with mass 1 500 kg travelling on a motorway at 130 km/h (approx. 36.1 m/s) has kinetic energy Ek = ½ × 1 500 × 36.1² ≈ 978 kJ. This enormous energy must be dissipated somewhere in a crash — which is why seatbelts, airbags, and crumple zones are so important. Example 3 — tennis ball: A tennis ball weighing 0.057 kg travelling at 50 m/s (180 km/h, a professional serve) has kinetic energy Ek = ½ × 0.057 × 50² = 71.25 J. Small mass but very high velocity produces significant energy.
Frequently asked questions
What is kinetic energy?
Kinetic energy is the energy an object possesses due to its motion. It depends on two factors: the mass of the object and its velocity. The formula is Ek = ½ · m · v². Any moving object — from a particle to a planet — has kinetic energy.
What is the kinetic energy formula?
The formula is Ek = ½ · m · v², where m is the mass in kilograms and v is the velocity in metres per second. The result is in joules (J). This is the classical (Newtonian) formula, valid for speeds much lower than the speed of light.
Why does kinetic energy depend on the square of velocity?
Kinetic energy grows with the square of velocity because the work-energy theorem states that Ek equals the net work done. For constant force, work = force × distance, and the stopping distance for an object moving at velocity v is proportional to v². This can be derived from Newton's second law and the kinematic equations.
How much kinetic energy does a car at 100 km/h have?
A car with a mass of 1 500 kg travelling at 100 km/h (27.78 m/s) has kinetic energy Ek = ½ × 1 500 × 27.78² ≈ 578 kJ. That is roughly the energy of 138 g of TNT. At 200 km/h the same car has four times more energy — about 2 312 kJ.
What is momentum and how does it differ from kinetic energy?
Momentum (p = m · v) is the product of mass and velocity, while kinetic energy (Ek = ½ · m · v²) depends on the square of velocity. Both describe motion, but momentum is a vector quantity conserved in all collisions, while kinetic energy is a scalar that is only conserved in perfectly elastic collisions.
In what units is kinetic energy measured?
Kinetic energy is measured in joules (J) in the SI system. In practice kilojoules (kJ), kilocalories (kcal), and watt-hours (Wh) are also used. The calculator provides the result in J, kJ, and kcal for convenience.
How does kinetic energy change during a car crash?
During a collision, kinetic energy is converted into plastic deformation energy (crumpling of bodywork), heat, sound, and vibration. A crash at twice the speed is four times more destructive because energy scales with the square of velocity — a key argument for lower speed limits in built-up areas.
What is the difference between kinetic and potential energy?
Kinetic energy is the energy of motion (Ek = ½mv²), while potential energy is the energy stored due to position or configuration (e.g. gravitational: Ep = mgh). Together they form mechanical energy, which is conserved in ideal (frictionless) systems. A swinging pendulum converts one into the other continuously.
How do I convert m/s to km/h?
Multiply metres per second by 3.6 to get kilometres per hour: v(km/h) = v(m/s) × 3.6. For example, 10 m/s = 36 km/h. The conversion factor 3.6 comes from the fact that 1 m/s = 3 600 m/h = 3.6 km/h.
Does a person running have significant kinetic energy?
A 70 kg person running at 10 m/s (36 km/h) has kinetic energy of 3 500 J (3.5 kJ). This is equivalent to the energy needed to power a 60 W light bulb for about 58 seconds. In competitive sport, speeds can be considerably higher, significantly increasing kinetic energy.
Results are for informational and educational purposes. The calculator uses the classical Newtonian formula and does not account for relativistic effects (relevant at velocities approaching the speed of light). For objects moving below 10% of the speed of light the formula is accurate to within 1%.