Calculate bullet muzzle velocity three ways: from kinetic energy (v=√(2E/m)), from a two-sensor chronograph (v=d/t), and velocity correction at distance X via ballistic coefficient. Includes verified 9mm, .45 ACP, 5.56 NATO, and .308 Win ammo presets from factory data. Everything is computed in your browser; nothing is uploaded.
⚠ Shooting safety — read first
Treat every firearm as loaded.
Never point the muzzle at anything you do not intend to shoot.
Keep your finger off the trigger until ready to fire; know your target and what is behind it.
For handloading: NEVER exceed published powder-manufacturer load data — overpressure loads can destroy the firearm and cause injury.
This calculator is purely an educational tool: not load data, not a substitute for official reloading manuals, and not tactical advice.
Verified ammo presets
Fills mass + energy (Mode 1) and muzzle velocity + BC (Mode 3) from factory data.
Mode 1 — From kinetic energy
v = √(2E/m). For when muzzle energy is known (e.g. from factory data) but velocity is not.
v = √(2E / m)
Muzzle velocity
0m/s
Muzzle velocity
0fps
Muzzle velocity
0km/h
Mode 2 — From chronograph
v = d/t. Enter the distance between two optical sensors and the bullet's time of flight between them.
v = d / t
Speed
0m/s
Speed
0fps
Speed
0km/h
Mode 3 — Downrange correction via ballistic coefficient
How fast is the bullet after traveling distance X? Simple exponential model v(x) = v₀·e−kx, with k derived from the G1 BC.
v(x) = v₀ · e−kx · k = ρ·Cd·π / (8·BC)
Speed at distance X
0m/s
Speed at distance X
0fps
Remaining speed
0%
Time of flight to X
0
Worked examples
Mode 1 — 9mm from energy: E=356 ft-lbf, m=115 gr
E = 356 × 1.35581795 = 482.67 J; m = 115 × 0.06479891 = 7.45187 g = 0.00745187 kg. v = √(2 × 482.67 / 0.00745187) = 359.92 m/s = 1,180.85 fps ≈ 1,181 fps (Federal box: 1,180 fps — difference from energy rounding).
Mode 2 — Chronograph: d=1 m, t=2.857 ms
v = 1 / 0.002857 = 350.02 m/s = 1,148.35 fps = 1,260.06 km/h.
Mode 3 — .308 Win: v₀=2,820 fps, BC=0.313, X=100 m
k = 1.225 × 0.44 × π / (8 × 0.313 × 703.06958) = 0.0009618/m. v(100) = 859.54 × e−0.09618 = 780.71 m/s = 2,561.40 fps (90.83% retained); time of flight = (e0.09618−1)/(k·v₀) = 122.12 ms.
Ammo presets — verification sources
Kaliber
Amunisi acuan
Massa
Muzzle velocity
BC G1
9mm Luger
Federal American Eagle 115gr FMJ
115 gr
1,180 fps
0.123
.45 ACP
FMJ 230gr kelas SAAMI (CCI Blazer / PMC)
230 gr
830 fps
0.153
5.56 NATO
M855/SS109 62gr (Lake City XM855, MIL-SPEC)
62 gr
3,025 fps
0.274
.308 Win
Federal Power-Shok 150gr SP (308A)
150 gr
2,820 fps
0.313
BC values: 9mm 0.123 (LuckyGunner computed from Federal 100-yard data); .45 ACP 0.153 (Speer TMJ RN 230gr, official Speer reloading data); M855 0.274 (Hornady, for contract M855 projectiles); .308 0.313 (Federal Power-Shok 150gr SP 308A). Preset velocities and energies are mutually consistent (E=½mv²): 356 / 352 / 1,260 / 2,648 ft-lbf per factory figures.
Metodologi
v = √(2E/m) · v = d/t · v(x) = v₀·e−kx · t(x) = (ekx−1)/(k·v₀)
Mode 1 is a direct inversion of E=½mv² — algebraically exact; its accuracy depends entirely on the accuracy of the energy data entered. Mode 2 assumes constant velocity between the two sensors; at short sensor spacing (≤1 m) the slowdown between sensors is negligible. Mode 3 uses an exponential drag model with constant G1 drag coefficient (Cd=0.44) and standard air density 1.225 kg/m³. This is an honest simplification: real drag depends on Mach number, so the model is accurate to ±5% at short-to-medium range (validated vs factory data: .308 Win at 100 yd off by 0.7%; 9mm at 100 yd off by 1.9%; .45 ACP at 50 yd off by 4.4%) but is not a substitute for factory ballistic tables or a full ballistic solver for long-range shooting. Unit conversions use exact definitions: 1 fps = 0.3048 m/s; 1 grain = 64.79891 mg; 1 ft·lbf = 1.35581795 J.
Scope limits: what is (and is not) calculated
This tool = MUZZLE VELOCITY. Three ways to compute v at/near the muzzle: from energy, from chronograph, and velocity correction at distance X via BC.
NOT a bullet energy calculator. To compute kinetic energy E=½mv² from mass and velocity, use bullet-energy (this tool is its inverse).
NOT a projectile trajectory calculator. For parabolic motion (drop time, horizontal distance, impact angle), use horizontal-projectile-motion (#1661).
NOT a full ballistic solver. For in-depth drag and ballistic coefficient analysis, use ballistic-coefficient.
Muzzle velocity is the speed of the projectile at the exact moment it leaves the firearm's barrel, usually stated in fps (feet per second) in the US or m/s in most of the world. In practice the chronograph is placed a few meters from the muzzle (typically ±3 m) so the muzzle blast does not false-trigger the sensors, then the result is corrected back to the muzzle.
What is the formula for computing velocity from kinetic energy?
From E = ½·m·v² we get v = √(2E/m). Enter energy in joules and mass in kilograms to get v in m/s. Example: E = 356 ft-lbf (482.67 J) and m = 115 grain (0.00745 kg) → v = √(2×482.67/0.00745) = 359.92 m/s ≈ 1,181 fps, matching the box figure of 1,180 fps (difference from rounding). This method is indirect: the result is only as accurate as the energy data you enter.
How does a ballistic chronograph work?
An optical chronograph uses two light sensors spaced d apart. The bullet breaks the first beam then the second; the device measures the time interval t, and velocity v = d/t. Example: sensors 1 m apart, time of flight 2.857 ms → v = 350.02 m/s. The result is the average velocity between the two sensors, so place the sensor midpoint exactly at the distance you want to measure.
Why does my chronograph result differ from the number on the ammo box?
Factory figures are measured in test barrels of standard length and condition, not in your firearm. A shorter barrel gives lower velocity because the gas pushes the bullet for less time — e.g. PMC X-TAC 62gr: 3,100 fps from a 20-inch barrel vs 2,920 fps from a 16-inch barrel. Powder temperature, lot-to-lot variation, and altitude also matter. A 2–5% deviation from the box figure is normal.
Does barrel length affect muzzle velocity?
Yes. Combustion gas pushes the bullet for as long as it is in the barrel, so a longer barrel generally gives higher velocity — with diminishing returns and an optimum that depends on caliber and powder type. PMC factory data for 5.56 NATO 62gr X-TAC: 3,100 fps (20″ barrel) dropping to 2,920 fps (16″ barrel), a 180 fps difference from just 4 inches of barrel.
What is the difference between fps and m/s?
Both are units of speed; 1 fps (foot per second) = 0.3048 m/s exactly, and 1 m/s = 3.6 km/h exactly. The US ammo industry uses fps (e.g. 9mm = 1,180 fps), while most of the world uses m/s (1,180 fps = 359.66 m/s). This calculator shows all three — m/s, fps, and km/h — so no manual conversion is needed.
What is ballistic coefficient and why does bullet velocity drop?
After leaving the barrel, the bullet is slowed by air resistance (drag). Ballistic coefficient (BC) measures how well the bullet retains velocity: BC = sectional density / form factor. The larger the BC, the more slowly velocity decays. This calculator's Mode 3 uses the simple exponential model v(x) = v₀·e^(−kx) with constant G1 drag — accurate to ±5% at short-to-medium range, but not a substitute for factory ballistic tables or a full ballistic solver for long-range shooting.
What is the typical muzzle velocity of each caliber?
Typical factory values (always dependent on the specific ammo and barrel): 9mm Luger 115gr FMJ ≈ 1,180 fps / 360 m/s (Federal American Eagle, 4″ barrel); .45 ACP 230gr FMJ ≈ 830 fps / 253 m/s (SAAMI standard, 5″ barrel); 5.56 NATO 62gr M855 ≈ 3,025 fps / 922 m/s (Lake City XM855, MIL-SPEC); .308 Win 150gr SP ≈ 2,820 fps / 860 m/s (Federal Power-Shok). Use the preset buttons in the calculator to fill these values automatically.
Can I measure muzzle velocity without a chronograph?
Indirectly, yes. If muzzle energy is known from trustworthy factory data, Mode 1 computes v = √(2E/m). Historically there was the ballistic pendulum: a bullet fired into a hanging block, with velocity computed from the swing height via conservation of momentum. But for practical accuracy the chronograph remains the standard — affordable nowadays and giving direct per-shot results.
What safety rules must be followed when shooting?
Four basic rules: (1) treat every firearm as loaded; (2) never point the muzzle at anything you do not intend to shoot; (3) keep your finger off the trigger until ready to fire; (4) know your target and what is behind it. For handloading: NEVER exceed published powder-manufacturer load data — overpressure loads can destroy the firearm. This calculator is purely an educational tool, not load data and not a substitute for official reloading manuals.
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