Formula and Method for Twist Rate (Greenhill's Rule)
A rifle barrel's twist rate describes how quickly the rifling spins a bullet, expressed as "1 turn in X inches" (for example, 1:10 means the bullet completes one full rotation for every 10 inches it travels down the bore). Spin stabilizes a bullet gyroscopically in flight, the same way a spinning top resists tipping over. Too slow a twist and the bullet tumbles in the air (yaws, keyholes on the target); too fast a twist over-stabilizes it and can, in extreme cases, stress the bullet's jacket. Sir Alfred George Greenhill, a British mathematician, developed an approximation in the 1880s for the Royal Small Arms Factory that is still the standard first-pass estimate used by shooters, gunsmiths, and bullet makers today.
How the calculation works
Greenhill's Rule states that the required twist rate T (in inches per turn) is T = C × D² / L, where D is the bullet's diameter in inches, L is its length in inches, and C is an empirical constant: 150 for muzzle velocities under 2,800 ft/s, or 180 for velocities of 2,800 ft/s and above (higher-velocity bullets need proportionally less spin to reach the same gyroscopic stability). The formula was calibrated for lead-core bullets, whose specific gravity is about 10.9; for bullets made of a different material, multiply the result by √(SG / 10.9), where SG is the bullet material's specific gravity — this calculator applies that correction automatically. Dividing the twist distance by the diameter gives the twist in "calibers" (bore diameters per turn), a unit-independent way to compare twist rates across calibers. Multiplying muzzle velocity by the spin imparted per inch of travel gives the bullet's spin rate in revolutions per minute (RPM) — a useful sanity check, since spin rates for common rifle cartridges typically fall in the 150,000-300,000 RPM range at the muzzle.
Common mistakes
- Mixing up faster and slower twist: a "faster" twist has a smaller second number — 1:7 spins a bullet more per inch of travel than 1:12, even though 7 is numerically smaller than 12.
- Ignoring bullet length: twist requirements depend on bullet length, not just caliber — within the same .308 caliber, a short 110-grain bullet and a long 208-grain bullet need noticeably different twist rates.
- Forgetting the specific-gravity correction: monolithic copper bullets (SG ≈ 8.9-9.1) are longer than a lead-core bullet of the same weight and caliber, so skipping the density correction can understate the twist a copper bullet actually needs.
- Treating Greenhill's Rule as exact: it is a well-tested approximation, not a substitute for a full gyroscopic stability calculation (such as the Miller twist rule) when working at the margins of stability.
Real-world applications
- Choosing a barrel twist rate when building or buying a rifle for a specific bullet weight range (for example, 1:8 for heavy 75-90 grain .224-caliber bullets versus 1:12 for lighter varmint bullets).
- Predicting whether a given factory barrel will stabilize a heavier or longer bullet than it originally shipped with.
- Estimating bullet RPM for handloaders concerned about jacket integrity or bullet material limits at very high spin rates.
- Comparing twist rates across different calibers on a common "calibers per turn" basis rather than raw inches.