Muzzle Velocity Calculator
Convert between projectile energy, mass, timing and launch speed, then see the speed in four units with energy, momentum and Mach number.
🎯 What is Muzzle Velocity?
Muzzle velocity is the speed of a projectile at the instant it leaves its launcher. In physics class it is simply the initial speed v0 of a projectile, and everything that follows (flight time, range, impact energy) depends on it. This calculator treats it as a pure kinematics and energy problem: given any one of three kinds of measurement, it finds the launch speed and then reports the related quantities, namely kinetic energy, momentum and the Mach number.
The three modes match the three ways people actually come by the number. In Energy and mass mode you know how much energy the launcher delivered, for example from a spring compression in a lab, or from a figure printed on a product or test sheet for an airsoft BB, a pellet or a foam dart, and you want the speed. In Chronograph mode you measured it directly: a timer started when the projectile crossed one gate and stopped when it crossed a second gate a known distance away. In Horizontal drop mode you launched the projectile sideways from a known height and measured how far away it landed, a classic classroom method that needs only a tape measure.
Because projectile specifications mix units, the calculator accepts energy in joules or foot-pounds, mass in grams, grains or kilograms, distance in metres, centimetres or inches, and time in milliseconds or microseconds. It reports speed in metres per second, feet per second, kilometres per hour and miles per hour. Two cautions apply. First, energy and speed are not interchangeable: the same energy gives very different speeds for different masses, and the relation is a square root, not a proportion. Second, a measured speed from a timer is an average over the gate gap, and a drop test ignores air drag, so each method carries its own small bias that the notes below the results explain.
The sanity note compares your result with the speed of sound, about 343 m/s in air at 20 C, and gives the Mach number. Almost all hobby and classroom launchers are comfortably subsonic, so a Mach number near or above 1 is a good hint that a unit was chosen wrongly. Pair this tool with the kinetic energy calculator, the projectile motion calculator for the flight path once you know v0, and the arrow speed calculator for a bow-specific estimate.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Airsoft BB at 1.0 J
A 0.20 g BB with 1.0 J of kinetic energy
Example 2 - Paintball timed between two gates
A 3.0 g paintball crosses gates 30 cm apart in 3.3 ms
Example 3 - Foam dart launched from a table
A 1.0 g foam dart leaves a launcher 1.0 m above the floor and lands 12 m away
Example 4 - Arrow energy given in ft-lbf and grains
A 400 grain arrow carrying 60 ft-lbf of kinetic energy
Example 5 - Physics class spring launcher
A compressed spring stores 0.90 J and launches a 25 g ball
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate muzzle velocity from energy and mass?
Rearrange kinetic energy KE = 1/2 m v^2 to get v = sqrt(2E/m), with energy in joules and mass in kilograms. A 0.20 g projectile (0.0002 kg) carrying 1.0 J moves at sqrt(2 x 1 / 0.0002) = 100 m/s, which is about 328 ft/s.
How do I convert ft/s to m/s?
Multiply feet per second by 0.3048 to get metres per second, since one foot is exactly 0.3048 m. For example 328 ft/s is about 100 m/s. To go the other way, divide metres per second by 0.3048.
How is projectile speed calculated from a chronograph?
A two gate chronograph measures the time t a projectile takes to cross a known gate spacing d. The average speed is v = d / t. A 30 cm gap crossed in 3.3 ms gives 0.30 / 0.0033 = 90.9 m/s.
How do you convert grains to grams or kilograms?
One grain is exactly 64.79891 milligrams, so grams = grains x 0.06479891. A 400 grain object is 25.92 g or 0.02592 kg. This calculator accepts grains directly and converts them internally.
How many joules is one foot-pound?
One foot-pound of energy is 1.3558179483314004 joules. So 60 ft-lbf is about 81.35 J. The calculator accepts either unit and shows the kinetic energy in both.
How do you find launch speed from a horizontal drop?
If a projectile leaves horizontally from height h, it falls for t = sqrt(2h/g) seconds while moving sideways at constant speed, so v = x / t. From 1 m up, landing 12 m away gives t = 0.4516 s and v = 26.57 m/s, ignoring air drag.
Does a heavier projectile always have more energy at the same speed?
Yes. At the same speed kinetic energy is proportional to mass, because KE = 1/2 m v^2. At the same energy, however, the heavier projectile is slower, and its momentum is larger because p = sqrt(2 E m).
What is the Mach number of a projectile?
Mach number is the projectile speed divided by the speed of sound. In air at 20 C the speed of sound is about 343 m/s, so 100 m/s is Mach 0.29. Values below about 0.8 are subsonic.
Why does the speed of sound change with temperature?
Sound travels faster in warmer air. A common approximation is 331 + 0.6 T metres per second with T in degrees Celsius, giving about 331 m/s at 0 C and 343 m/s at 20 C. The Mach number you see here uses 343 m/s.
How accurate is a drop test compared with a chronograph?
A drop test is a rough check. Air drag, launch angle error and the difficulty of measuring the landing point all shift the result, and drag makes the true launch speed higher than the estimate. A two gate timer is usually the better tool.
What is the difference between kinetic energy and momentum?
Kinetic energy is 1/2 m v^2 and grows with the square of speed. Momentum is m v and grows linearly. At equal energy, a heavier and slower projectile carries more momentum than a lighter and faster one.