Kinetic Energy Calculator (KE = ½ m v²)
Enter a mass and speed to get the kinetic energy (KE) — the energy a moving object carries, equal to ½ × mass × speed². The result is shown in joules (J), kilojoules (kJ), kilocalories (food calories), foot-pounds force (ft·lbf) and watt-hours (Wh), so you can compare across cars, bullets, athletes and appliance energy use.
Enter a valid mass and a non-negative speed.
Kinetic energy (KE)
—
—
Other units
- Kilojoules
- —
- Kilocalories (food calories)
- —
- Foot-pounds force
- —
- Watt-hours
- —
1 Wh = 3600 J — handy for comparing against household appliance energy use.
Formula
KE = ½ · m · v² (m in kg, v in m/s, result in J = kg·m²/s²)
Kinetic energy scales with the square of speed — double the speed and energy quadruples. Inputs are normalised to kg and m/s before the formula is applied.
Formula
KE = ½ · m · v² // m in kg, v in m/s, KE in J (kg·m²/s²) 1 J = 1 N·m = 1 kg·m²/s² 1 kJ = 1000 J 1 kcal = 4184 J // food calorie 1 ft·lbf ≈ 1.3558 J 1 Wh = 3600 J
- · Square-of-speed scaling: doubling the speed quadruples the energy; tripling it gives 9× the energy. So going from 50 to 100 km/h multiplies crash energy by 4×, not 2×.
- · Inputs are normalised to kg and m/s before the formula is applied: 1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s (NIST SP 811).
- · A useful intuition: 1 joule = 1 N·m ≈ the work needed to lift a 100 g object 1 m; 1 kJ ≈ lifting a 1 kg mass 102 m.
- · Car example: a 1500 kg sedan at 100 km/h carries ~579 kJ — equivalent to 138 food calories. Stopping in a wall transfers all of that into the body, airbags and occupants.
- · Bullet example: a 5 g lead bullet at 400 m/s carries ~400 J (typical 9 mm Parabellum class); a BB gun pellet is usually < 7.5 J.
- · This is classical (Newtonian) kinetic energy, accurate while v is well below the speed of light. Near c you need the relativistic form KE = (γ−1)·m·c², which this tool does not handle.
- · Mass must be ≥ 0; negative speed is squared so it gives the same energy as the equivalent positive value. Empty fields, negative mass or non-numeric input show an error.
- · Sources: Halliday, Resnick & Walker, "Fundamentals of Physics", chapter 7; NIST Special Publication 811 (2008) unit conversions.
Frequently asked
How much kinetic energy does a 1500 kg car at 100 km/h carry?
100 km/h ≈ 27.78 m/s. Plugging in: KE = ½ × 1500 × 27.78² ≈ 578 700 J ≈ 578.7 kJ ≈ 138.3 kcal. In a crash, the car has to dissipate roughly a quarter of the energy in a Big Mac (≈ 550 kcal). Bump the speed to 120 km/h (33.33 m/s) and KE jumps to ≈ 833 kJ — a 44 % increase, not 20 %.
If I double the speed, by how much does the kinetic energy go up?
It quadruples. The v in KE = ½ m v² is squared, so v → 2v gives 4× the energy, and v → 3v gives 9×. That's why crash forces, braking distance and running injury risk all scale with the square of speed — a small bump in speed produces a much bigger jump in energy.
How do joules and food calories (kcal) relate?
One food calorie equals 4184 joules (the international thermochemical definition). So a 100 kcal apple holds 418 400 J of chemical energy — roughly the kinetic energy of throwing your own 70 kg body at 109 km/h. The "kcal" row in this calculator just divides joules by 4184 so you can compare against food labels at a glance.
Why does kinetic energy turn into heat, sound and deformation?
Conservation of energy. When a moving object is brought to rest (a car hitting a wall, a bullet stopping in wood), its kinetic energy doesn't vanish — it converts into permanent deformation of metal, friction heat, sound waves and a tiny bit of light. The higher the kinetic energy, the more "somewhere" you need for it to go before it reaches the occupants. That's the entire reason crumple zones and airbags exist.
Related tools
Ohm's Law Calculator (V / I / R / P)
Enter any two of voltage, current, resistance, or power — the calculator solves for the other two using V = IR and P = VI.
Speed, Distance & Time Calculator
Enter any two of distance, time and speed to get the third — with km/h, mph, m/s, km, miles, hours and minutes supported.
Density Calculator (mass / volume)
Compute density from mass and volume (ρ = m / V), or solve for the missing variable. Built-in reference table for 19 common substances.
Projectile Motion Calculator
Enter launch speed, angle and height to compute projectile range, peak height and flight time (no air resistance). Pick from Earth, Moon, Mars and more.
Wind Chill Calculator
Compute the wind chill (feels-like temperature) from air temperature and wind speed using the 2001 Environment Canada / US NWS formula, with frostbite risk levels.
Dew Point Calculator
Compute dew point from air temperature and relative humidity using the Magnus formula — handy for HVAC, photography and weather analysis.
Half-Life & Exponential Decay Calculator
Enter any three of initial amount, remaining amount, elapsed time and half-life to solve for the fourth — useful for radioactive decay, drug pharmacokinetics and radiometric dating.
Resistor Color Code Calculator (4 / 5 band)
Pick the colour bands and instantly read the resistance and tolerance — 4-band and 5-band notations supported, with Ω / kΩ / MΩ formatting and a closest E12 / E24 preferred-value check.
GPS Distance Calculator (Haversine)
Enter two latitude/longitude pairs to compute the great-circle distance using the haversine formula (km, miles, nautical miles), with bearing and midpoint.
Solution Dilution Calculator (C₁V₁ = C₂V₂)
Solve any one of C₁, V₁, C₂, V₂ from the dilution equation C₁V₁ = C₂V₂ — a daily lab essential for chemistry, biology and pharmacy work.
Decibel (dB) Sum Calculator
Two 80 dB sound sources do not equal 160 dB. Enter multiple dB values to compute the combined SPL, and subtract background noise to recover the signal alone.
Resistor Parallel / Series Calculator
Enter up to 8 resistor values to see the series total (R₁ + R₂ + …) and the parallel total (1 / Σ(1/Rᵢ)) at the same time.
Wavelength ↔ Frequency Calculator
Convert between electromagnetic wavelength and frequency via c = λf, with the matching spectrum band (radio / microwave / visible / X-ray / γ) and photon energy.
Tank Volume Calculator
Compute the capacity of vertical or horizontal cylindrical, rectangular and spherical tanks, including partial-fill volumes at a given liquid level.
Pendulum Period Calculator (T = 2π√L/g)
Enter the pendulum length and local gravity to get the period, frequency and angular frequency, with Earth/Moon/Mars/Jupiter presets — and reverse-solve for the length needed to hit a target period.
Heat Index Calculator
Enter air temperature and relative humidity to get the apparent temperature (NOAA Rothfusz heat index) and the corresponding heat-stress risk band.
Vehicle Stopping Distance Calculator
Enter speed, reaction time and road friction to estimate reaction, braking and total stopping distance.
Snell's Law Refraction Calculator
Enter the refractive indices of two media and an angle of incidence — get the refraction angle and critical angle from Snell's law (n₁ sin θ₁ = n₂ sin θ₂).
Capacitor Energy Calculator
Enter capacitance (F, mF, µF, nF, pF) and voltage to compute the stored energy (E = ½CV²) and charge (Q = CV) on a capacitor.
Boiling Point at Altitude Calculator
Enter altitude to compute the boiling point of water (°C / °F) and local air pressure using the ICAO standard atmosphere and the Antoine equation — useful for hiking, cooking and high-altitude baking.
Specific Heat (Q = mcΔT) Calculator
Solve Q = m × c × ΔT for any one of heat energy, mass, specific heat capacity or temperature change — with presets for water, aluminium, iron, copper, glass, air and more.
pH and Hydrogen Ion Concentration Calculator
Convert between pH, pOH, hydrogen-ion concentration [H⁺] and hydroxide concentration [OH⁻] — with acid / neutral / alkaline classification.
Ideal Gas Law (PV = nRT) Calculator
Pick the unknown (P, V, n or T), enter the other three and PV = nRT is solved instantly — works in Pa / kPa / atm / bar / mmHg / psi, m³ / L / mL, mol / mmol / kmol and K / °C / °F.