Impact Energy Calculator finds impact energy from mass and speed or drop height, then gives the average and peak impact forces and g-force from stopping distance or collision time.
Enter the mass, its speed at impact and the distance it takes to stop.
Result Unit
Impact Diagram
Not to scale. The dashed box is the collision distance: the shorter it is, the higher the force for the same energy.
Step-by-Step Working
- Formula: E = ½ × m × v²
- Convert to SI: d = 0.02 m
- Average force: F = m × v² ÷ (2 × d) = 90 kg × (5 m/s)² ÷ (2 × 0.02 m) = 56,250 N
- Deceleration: a = F ÷ m = 625 m/s², which is 63.73226 g
- Energy: E = ½ × 90 kg × (5 m/s)² = 1,125 J
Force by Distance
| Distance (cm) | Avg force (kN) | g-force |
|---|---|---|
| 0.5 | 225 | 254.9 |
| 1 | 112.5 | 127.5 |
| 2 | 56.25 | 63.73 |
| 4 | 28.13 | 31.87 |
| 8 | 14.06 | 15.93 |
| 20 | 5.625 | 6.373 |
What the Impact Energy Calculator Works Out
The Impact Energy Calculator finds the energy a moving or falling object carries into a collision, then turns it into the force and deceleration of the hit. Energy depends only on mass and speed, but force depends on how quickly the object is stopped, so the tool asks for both.
A menu picks how the impact is described. Velocity and Distance takes the speed at contact and the distance the object travels while stopping. Velocity and Time takes the speed and the duration of the collision. Drop Height and Distance takes the height of a fall instead of a speed. Force and Distance works the other way, from a measured average force to the energy behind it.
Mass can be typed in kilograms, grams, pounds or metric tons, and speed in m/s, km/h, mph or ft/s. The default is a 90 kg mass at 5 m/s stopping in 2 cm. The Impact Energy Calculator shows 1,125 J delivered, an average force of 56.25 kN and a deceleration of 63.73 g.
Impact Energy Formula
Impact energy is the kinetic energy an object has at the moment it strikes. For one moving object hitting something at rest, that is the whole of the impact energy.
$$E = \frac{1}{2} m v^2$$
E is in joules when m is in kilograms and v is in meters per second. For the default case, ½ × 90 × 5² gives 1,125 J. Speed counts twice in the formula, so doubling the speed of an impact quadruples its energy, while doubling the mass only doubles it.
For a dropped object, the energy at impact equals the potential energy it had at the top. This is the falling object version of the impact energy formula.
$$E = m g h$$
The tool uses standard gravity, g = 9.80665 m/s², the value fixed in the NIST conversion tables. A 90 kg mass dropped 1.2 m arrives with 90 × 9.80665 × 1.2 = 1,059 J. Air resistance is ignored, which is close for dense objects over short drops.
What is the formula for impact speed?
The speed just before impact comes from the same energy balance. Setting mgh equal to ½mv² and cancelling the mass gives the impact speed, which does not depend on how heavy the object is.
$$v = \sqrt{2 g h}$$
A 1.2 m drop lands at 4.85 m/s. In Velocity mode the third result card runs this the other way and shows the drop height that would give your speed. For the default 5 m/s it is 1.275 m, reached after a fall of 0.51 s, which helps when setting up a drop test to match a horizontal impact.
Impact Force From Distance or Time
The energy is fixed by mass and speed, but the force is not. The same impact can be gentle or violent depending on how far or how long the object takes to stop. This is the impact force calculator side of the tool.
When the stopping distance is known, the work-energy theorem gives the average force. The surface has to do work equal to the impact energy over that distance.
$$F_{avg} = \frac{E}{d} = \frac{m v^2}{2 d}$$
OpenStax University Physics works this with a 2.60 g bullet at 335 m/s that stops in 15.2 cm of pine boards. Its 145.9 J of energy over 0.152 m gives an average force of about 960 N. Enter the same figures in the Impact Energy Calculator and it returns 959.8 N, a stop lasting 0.91 ms.
When the collision time is known instead, the impulse-momentum theorem gives the average force as the change in momentum divided by the time. Crash tests and sensor logs often report time rather than crush distance.
$$F_{avg} = \frac{m v}{t}$$
The OpenStax chapter on impulse uses an 87.8 kg driver moving at 27 m/s. Stopped in 0.20 s, he feels an average force of 11,853 N, about 14 times his weight. The Velocity and Time mode gives the same 11.85 kN, with 32 kJ of impact energy and a deceleration of 13.77 g.
Both formulas give an average. The first result card also lists a peak force at twice the average. That peak applies when the force builds evenly from zero, the way a spring or a crumple zone resists, because the energy is then the area of a triangle rather than a rectangle. The Elastic Potential Energy Calculator uses the same triangle.
Falling Object Impact Force
Drop Height and Distance mode turns the Impact Energy Calculator into a falling object impact force calculator. A 90 kg mass falling 1.2 m and stopping in 2 cm arrives with 1,059 J, and spreading that over 0.02 m gives an average stopping force of 52.96 kN. The deceleration is 60 g, which is simply the drop height divided by the stopping distance.
HyperPhysics at Georgia State University points out that the object keeps falling while it stops, so the height should include the stopping distance. In practice this means the ground carries the object’s weight on top of the stopping force. For this example that adds 883 N. The first result card shows both figures in this mode, 52.96 kN as the average stopping force and 53.84 kN on the surface, with weight.
G-Force of an Impact
The second result card of the Impact Energy Calculator divides the average force by the mass to get the deceleration, then expresses it as a multiple of standard gravity. That multiple is the g-force of the impact.
$$g_{force} = \frac{a}{9.80665} = \frac{v^2}{2 d \times 9.80665}$$
The default impact decelerates at 625 m/s², which is 63.73 g. A longer stop lowers this in direct proportion. The Force by Distance table under the results shows the same 1,125 J at stopping distances from 0.5 cm to 20 cm, where the g-force falls from 254.9 g to 6.37 g.
How much is 1 kg force?
One kilogram-force is the weight of one kilogram under standard gravity, exactly 9.80665 N. A 60 kg person at rest therefore presses down with 588.4 N, and the kg to Newtons Calculator does that conversion for any mass.
During an impact the g-force multiplies that weight. At 50 g, each kilogram pushes with 50 kgf, which is 490.3 N. A 60 kg body at 50 g pushes with 3,000 kgf, or about 29.4 kN, which is why stopping distance matters so much for anything carried in a crash.
How Far Is a Fall in Seconds?
Many impact questions start with a fall time rather than a height. Without air resistance, the distance fallen grows with the square of time, d = ½gt², and the speed grows in step with time, v = gt.
| Fall time | Distance fallen | Speed reached |
|---|---|---|
| 1 s | 4.9 m (16.1 ft) | 9.8 m/s (32.2 ft/s) |
| 2 s | 19.6 m (64.3 ft) | 19.6 m/s (64.3 ft/s) |
| 3 s | 44.1 m (144.8 ft) | 29.4 m/s (96.5 ft/s) |
| 4 s | 78.5 m (257.4 ft) | 39.2 m/s (128.7 ft/s) |
So 2 seconds of falling covers about 64 feet, and a 3 second fall is about 145 feet. Gravity is 32.174 ft/s², which is the “32 feet per second” people quote. It is an acceleration, so the speed rises by about 32 ft/s every second.
Past a few seconds, air resistance takes over. The same formula would give 788 ft after 7 s, 2,317 ft after 12 s and 6,435 ft after 20 s, and a 30,000 ft drop in 43 s. Real falls are shorter in distance and longer in time than that, because drag caps the speed. The Free Fall with Air Resistance Calculator handles those long falls, and the Free Fall Calculator covers the short ones.
Impact Energy Unit
The SI unit of impact energy is the joule, one newton acting over one meter. Joules are the default in the Impact Energy Calculator, and the result unit menu also offers kilojoules, foot-pounds and inch-pounds.
Foot-pounds and inch-pounds still appear on many US drop-test and material-test reports. One joule is 0.7376 ft·lbf or 8.851 in·lbf, so the default 1,125 J reads as 829.8 ft·lbf. The fourth result card lists the energy in three units at once.
Force is a different quantity with its own unit. The tool gives it in newtons or kilonewtons, with pounds-force alongside, and the two should never be mixed. A joule of energy only becomes a newton of force once you divide by a stopping distance in meters.
Impact Loads and Impact Tests
What is impact energy?
Impact energy is the kinetic energy a body brings into a collision. When a moving object hits something at rest, all of its kinetic energy has to go somewhere during the impact, into deformation, heat, sound or a rebound.
The figure is the same whether the object is a hammer, a dropped part or a vehicle. What changes from case to case is how that energy is absorbed, which sets the force and the damage.
What is impact loading?
Impact loading is a large force applied over a very short time, as opposed to a load that builds slowly. A 1,125 J impact stopped in 2 cm loads a surface with 56 kN for 8 ms, while the same mass resting on it loads it with less than 1 kN.
Engineers design for impact loads by adding stopping distance. Padding, crumple zones, rubber bumpers and energy-absorbing barriers do not reduce the energy. They spread it over more distance or time, which lowers the peak force.
How is impact force measured?
Impact force is measured directly with a load cell or force plate under the struck surface, or worked out from an accelerometer on the moving object using F = ma. High-speed video can give the impact velocity and the stopping distance.
Those two measured numbers are what the Impact Energy Calculator needs. With them, it turns a measured speed and crush distance into an average force and deceleration you can compare with a design limit.
What are the two types of impact tests?
The two standard impact tests for metals are the Charpy and the Izod test. ASTM E23 covers both, describing Charpy as a simple-beam test and Izod as a cantilever-beam test on a notched bar.
In both, a swinging pendulum breaks the specimen. The energy absorbed equals the pendulum’s weight times the difference between its drop height and its rise height after the break. The result, in joules or ft·lbf, is often called the impact strength or impact value of the material.
How do you convert force to energy?
Energy is force times the distance it acts over, E = F × d, as long as the force is steady. An average force of 500 N over 0.3 m is 150 J. If the force builds evenly from zero instead, the energy is half the peak force times the distance.
The Force and Distance mode of the Impact Energy Calculator is the force to energy calculator. Enter the average force, the collision distance and the mass. Its default of 50 kN over 2 cm on 90 kg gives 1,000 J, an impact velocity of 4.714 m/s and a deceleration of 56.65 g, and its table shows how the energy and speed grow with distance.
For collisions that involve momentum more than energy, the Impulse and Momentum Calculator works from force and time. The Car Crash Calculator applies these ideas to a person in a vehicle collision.
Is there an impact energy calculator app?
The Impact Energy Calculator runs in a phone browser with nothing to install, and the math runs on your device. The inputs stack one per row on a small screen, and the result cards stay readable on a phone.
Copy Results and Print Results save the energy, force and step-by-step working for a test log. Other energy tools sit on the energy, work and power calculators hub, including the Bullet Energy Calculator for projectile impacts.