Bullet Energy Calculator
Turn a projectile's mass and speed into kinetic energy and momentum, or work backwards from energy to speed, in SI and US units.
💨 What is Projectile Kinetic Energy?
Kinetic energy is the energy a moving object has because of its motion. For any projectile, whether it is an airsoft BB, an air-gun pellet, a paintball, a foam dart or a thrown baseball, the classical value is half the mass times the speed squared. It is measured in joules (J) in the SI system, and in the United States it is often quoted in foot-pounds of energy (ft-lbf). This calculator takes a mass and a speed in whichever units you have, converts both to SI, and reports the energy in joules and foot-pounds. It treats the question purely as classical mechanics and unit conversion.
Alongside energy, the tool gives momentum, the product of mass and velocity, in kg·m/s together with the identical value in newton seconds. It also gives the Mach number against a reference speed of sound of 343 m/s, and a plain-language comparison: the height from which a 1 kg mass would have to fall to arrive with the same energy. That last figure is a handy way to feel the size of a number in joules, since a 1 J projectile equals a 1 kg weight dropped about 10 cm.
There are two modes. In Mass and speed mode you enter what you know about the projectile and read off the energy. In Speed from energy mode you go the other way, entering an energy and a mass to find the speed. That reverse direction is the same relation covered in more depth, with chronograph timing and horizontal drop methods, in the muzzle velocity calculator, so use that page when you want to measure the speed rather than convert it.
Three ideas are worth keeping straight. First, energy depends on the square of speed, so a small change in speed has a large effect on joules. Second, energy and momentum are different quantities: two projectiles can share the same energy yet differ several times over in momentum when their masses differ. Third, the numbers here describe a projectile in motion, not what it does on contact, which depends on many other factors that are outside the scope of a mechanics page. For related tools see the kinetic energy calculator, the momentum calculator and the arrow speed calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
The masses and speeds below are illustrative inputs chosen for round numbers, not published specifications of any product.
Example 1 - Airsoft BB at 100 m/s
A 0.20 g BB travelling at 100 m/s
Example 2 - Air-gun pellet at an illustrative speed
A 0.50 g pellet at 120 m/s (illustrative input)
Example 3 - Thrown baseball
A 145 g baseball thrown at 40 m/s (about 89 mph)
Example 4 - Foam dart: same energy, more momentum
A 5 g foam dart at 20 m/s
Example 5 - Speed from energy and mass
Working backwards from 116 J on a 145 g mass
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the kinetic energy of a projectile?
Use KE = 1/2 m v^2 with mass in kilograms and speed in metres per second. A 0.20 g pellet (0.0002 kg) at 100 m/s has KE = 0.5 x 0.0002 x 100^2 = 1.0 J, which is about 0.738 ft-lbf.
How do you convert joules to foot-pounds?
Divide joules by 1.3558179483314004 to get foot-pounds of energy. So 100 J is about 73.76 ft-lbf, and 100 ft-lbf is about 135.58 J.
How do you find speed from energy and mass?
Rearrange KE = 1/2 m v^2 to v = sqrt(2E/m). With 116 J and a 145 g mass (0.145 kg) the speed is sqrt(2 x 116 / 0.145) = 40 m/s.
What is momentum and how is it calculated?
Momentum is mass times velocity, p = m v, in kg m/s. A 0.145 kg ball at 40 m/s has p = 5.8 kg m/s. One newton second is the same as one kg m/s.
How many grains are in a gram?
One grain is exactly 64.79891 mg, so one gram is about 15.4324 grains. A 100 grain mass is 6.4799 g or 0.0064799 kg.
Does doubling speed double the energy?
No, it quadruples it. Kinetic energy grows with the square of speed, so 2 times the speed gives 4 times the energy, while 2 times the mass gives only 2 times the energy.
What is the difference between energy and momentum?
Energy is a scalar equal to 1/2 m v^2 in joules. Momentum is a vector equal to m v in kg m/s. Two objects can share the same energy but have different momentum if their masses differ.
What is the Mach number of a projectile?
Mach number is speed divided by the speed of sound. In air at 20 C that is about 343 m/s, so 100 m/s is Mach 0.29.
How high must a 1 kg mass fall to gain the same energy?
Use h = E / (m g) with m = 1 kg and g = 9.80665 m/s^2. An energy of 1 J equals a 1 kg mass falling 10.2 cm, and 116 J equals a fall of 11.83 m.
Is the kinetic energy formula exact at any speed?
No. KE = 1/2 m v^2 is the classical result and is very accurate for everyday speeds. Near a large fraction of the speed of light the relativistic expression is needed.