Solve for kinetic energy, mass, or velocity using KE = ½ m v². Change any value to recalculate instantly, with unit conversion and a step-by-step walkthrough.
Kinetic Energy
500J
Same mass, different speed
0.5× v
125.0 J
1× v
500.0 J
1.5× v
1.1 kJ
2× v
2.0 kJ
Double the speed and the energy goes up four times, not twice — which is why stopping distance grows so sharply with speed.
How is this calculated?
KE = ½ · m · v²
1. Mass in SI: 10 kg = 10 kg
2. Velocity in SI: 10 mps = 10 m/s
3. KE = ½ × mass × velocity² = 500 J
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About the Kinetic Energy Calculator
Kinetic energy is the energy an object possesses because it is moving, defined as one half its mass multiplied by the square of its speed. That squared term is the single most important feature of the formula and the source of most of its practical consequences. Because energy scales with the square of speed rather than proportionally, doubling a vehicle's speed does not double its kinetic energy — it quadruples it, which is why braking distances grow so sharply with speed and why the severity of a collision rises far faster than the speedometer reading suggests. Kinetic energy is measured in joules, is always positive or zero regardless of direction of travel, and forms one half of the mechanical energy of a system alongside potential energy. The work-energy theorem ties it directly to force: the net work done on an object equals exactly the change in its kinetic energy, which makes it one of the most useful quantities in all of mechanics.
Mathematical Formula & Logic
Kinetic energy depends on mass and on the square of speed.
1. Translational kinetic energy:
KE = ½ · m · v²
Where m is mass in kilograms and v is speed in metres per second.
The result is in joules (J), where 1 J = 1 kg·m²/s².
2. Solving for speed:
v = √(2 · KE / m)
3. Solving for mass:
m = 2 · KE / v²
4. Relationship to momentum:
p = m · v
KE = p² / (2m)
5. The work-energy theorem:
W_net = ΔKE = ½m·v² − ½m·u²
The net work done on a body equals its change in kinetic energy.
6. Rotational kinetic energy:
KE_rot = ½ · I · ω²
Where I is moment of inertia and ω is angular velocity.
7. The scaling consequence:
Double the speed -> 4x the kinetic energy
Triple the speed -> 9x the kinetic energy
Double the mass -> 2x the kinetic energy
Step-by-Step Example
Compare the kinetic energy of a 1,500 kg car at 50 km/h and at 100 km/h to see why speed dominates:
At 50 km/h
1. Convert to SI: 50 ÷ 3.6 = 13.889 m/s
2. KE = ½ × 1,500 × (13.889)²
3. (13.889)² = 192.90
4. KE = 0.5 × 1,500 × 192.90 = 144,675 J ≈ 144.7 kJ
At 100 km/h
5. Convert to SI: 100 ÷ 3.6 = 27.778 m/s
6. (27.778)² = 771.60
7. KE = 0.5 × 1,500 × 771.60 = 578,700 J ≈ 578.7 kJ
The comparison
8. Ratio = 578,700 ÷ 144,675 = 4.0 exactly
9. Doubling the speed multiplied the energy by four, not by two.
Why this matters for braking
10. Brakes dissipate kinetic energy as heat, and the work done is force × distance. With the same braking force available, stopping from 100 km/h requires four times the distance of stopping from 50 km/h, not twice. This single relationship explains why speed limits fall disproportionately in areas where stopping distance is critical, and why a modest speed reduction produces a large safety gain.
Reference Data & Values
object
mass kg
speed m_s
kinetic energy
Tennis ball served
0.058
58.0
97.6 J
Sprinter
75
10.4
4,056 J
Cyclist
90
8.0
2,880 J
Car at 50 km/h
1,500
13.889
144.7 kJ
Car at 100 km/h
1,500
27.778
578.7 kJ
Truck at 100 km/h
40,000
27.778
15.4 MJ
Rifle bullet
0.004
900
1,620 J
Jet airliner (cruise)
250,000
250
7.81 GJ
Frequently Asked Questions
Because speed enters the formula as a square rather than linearly. In KE = ½mv², replacing v with 2v gives ½m(2v)², and since (2v)² equals 4v², the whole expression becomes four times larger. Tripling the speed multiplies energy by nine, and so on. This is the most consequential feature of the equation in practice: it means a car at 100 km/h carries four times the destructive energy it had at 50 km/h, and needs four times the distance to shed it under the same braking force.
No. Mass is always positive and the velocity term is squared, so any non-zero velocity produces a positive result regardless of direction. An object moving at −20 m/s has exactly the same kinetic energy as one moving at +20 m/s, because squaring eliminates the sign. The minimum possible value is zero, reached only when the object is at rest. This is a genuine difference from velocity and momentum, both of which are vectors and can be negative.
Kinetic energy is energy of motion, determined by mass and speed, while potential energy is stored energy determined by position or configuration, such as height in a gravitational field or the compression of a spring. The two convert into one another continuously while their sum, the total mechanical energy, stays constant when no friction or other dissipative force acts. A falling object trades gravitational potential energy for kinetic energy on the way down, and a pendulum cycles between the two at every swing.
It states that the net work done on an object equals its change in kinetic energy, written W_net = ΔKE. Since work is force multiplied by displacement, the theorem provides a direct bridge between forces and motion without needing to track acceleration through time. It is what allows a braking problem to be solved by asking how much energy must be dissipated over what distance, and it explains why stopping distance scales with the square of speed while stopping time scales only linearly.
Because kinetic energy is directly proportional to mass, and a fully loaded truck can weigh well over twenty times a typical car. At 100 km/h a 40,000 kg truck carries about 15.4 MJ against roughly 578.7 kJ for a 1,500 kg car — around twenty-seven times more energy at identical speed. Since brakes must dissipate all of it, this is why heavy vehicles need far longer stopping distances and why speed limits and following distances are set more conservatively for them.
The classical formula KE = ½mv² is an approximation that becomes inaccurate as speeds approach a significant fraction of the speed of light. The relativistic expression is KE = (γ − 1)mc², where γ is the Lorentz factor 1/√(1 − v²/c²). At everyday speeds the two agree to many decimal places, so the classical form is entirely adequate for vehicles, projectiles and sports. The difference only becomes material above roughly ten percent of light speed, which is the domain of particle accelerators rather than engineering.