Ballistic Bore Projectile Speed Calculator

Muzzle velocity from barrel: v = √(2·P·V/(m·γ))

As a first cut at interior ballistics, you can treat the projectile as something accelerated by propellant gases expanding inside the barrel: v = √(2·P·V/(m·γ)), where P is the average chamber pressure (Pa), V the swept volume (m³), m the projectile mass (kg) and γ the polytropic ratio of the combustion gases (≈ 1.2–1.4). For reference, typical muzzle velocities run 9 mm Luger ~360 m/s, 5.56×45 NATO ~940 m/s, .50 BMG ~900 m/s and .308 Winchester ~840 m/s. Worked example: with P = 250 MPa, V = 8 cm³ = 8e-6 m³, m = 4 g = 0.004 kg, γ = 1.3 → v ≈ √(2·2.5e8·8e-6/(0.004·1.3)) ≈ 877 m/s.

Applications

Forensic ballistics relies on it to estimate muzzle velocity from cartridge data in criminal investigations and trajectory reconstruction. Defence and military procurement use it when specifying chamber pressure and barrel length for new service rifles. In competitive shooting (IPSC, CBC Brazil and ISSF disciplines) reloaders lean on it to tune powder charge against velocity nodes. It also turns up in ammunition R&D, barrel manufacturing tolerances, hunting load development, and pressure-test programmes such as CIP and SAAMI proof loads.

FAQ

Why does a longer barrel give higher velocity? V grows with barrel length, so the projectile gets pushed by the expanding gases for longer. That's why carbines (10–14") come in 50–150 m/s slower than full rifles (20–24") firing the same load.

Is the average pressure realistic? Not really, since the formula collapses everything into a single average P, whereas a real pressure curve spikes fast and then decays. For accuracy, tools like QuickLOAD and Lapua integrate the full P(t). Think of the √ formula as an order-of-magnitude check.

Why does γ matter? γ captures how the hot gases release energy as they expand. Smokeless powder tends to land around γ ≈ 1.25, so plugging in 1.4 (the value for air) will undershoot the velocity by a few percent.