Twist Rate & Bullet Stability Calculator: Miller Sg, Greenhill and the Twist You Need
Check whether a barrel twist stabilises your bullet with the Miller formula: gyroscopic stability factor Sg from bullet length, weight, calibre and velocity, corrected for temperature and station pressure or altitude, with a plastic-tip allowance. Shows the twist needed for Sg 1.4, 1.5 and 2.0, the longest bullet your barrel stabilises, the Greenhill rule, spin rpm and an Sg-by-twist table.
How it works
Miller: Sg = 30 m ÷ [t² d³ l (1 + l_m²)] × (v ÷ 2,800)^⅓ × [(T + 460) ÷ 519] × (29.92 ÷ P), with m in grains, d in inches, t = twist in calibres, l = total length in calibres, l_m = metal length in calibres (l_m = l without a plastic tip; Courtney & Miller 2012), v in ft/s, T in °F, P = station pressure in inHg · twist for a target Sg = d × √(30 m × factors ÷ [Sg d³ l (1 + l²)]) · Greenhill: twist = 150 d² ÷ L (180 above 2,800 ft/s) × √(SG ÷ 10.9) · rpm = v × 12 ÷ twist × 60
A bullet flies point-first only if it spins fast enough to resist the air’s overturning moment. Don Miller’s 2005 formula estimates the gyroscopic stability factor Sg from the bullet’s weight, calibre and length and the barrel twist. Length dominates: the overturning moment grows with length much faster than the spin inertia does, so long, heavy-for-calibre and monolithic copper bullets need faster twists. Sg below 1.0 tumbles. From 1.0 to 1.4 the bullet flies but wobbles, which costs ballistic coefficient and accuracy. Bryan Litz’s testing found BC reaches its full value only at about Sg 1.5 or more. Very high values do little harm except to thin-jacketed varmint bullets, which can come apart at extreme rpm. Velocity helps a little (Sg rises with the cube root of speed), and dense air hurts: cold temperatures and high pressure (low altitude) lower Sg, so the winter, sea-level combination is the one to check. Enter the real station pressure, or choose Altitude to use the ICAO standard atmosphere. The calculator also solves the formula backward. It gives the twist you need for Sg 1.4, 1.5 and 2.0, and the longest bullet of the same weight your barrel will stabilise to 1.5. Greenhill’s 1879 rule (150 × d² ÷ length, or 180 above 2,800 ft/s) is shown for comparison; it suits short lead bullets but tends to under-twist long modern designs. Plastic tips add length but almost no mass. Following Courtney and Miller (2012), the total length stays in the first length term and only the metal part is used in the (1 + l²) term, which raises Sg compared with counting the full length.
Worked example
A 175 gr .308 bullet 1.24 in long at 2,650 ft/s in a 1:10 in twist, at 59 °F and 29.92 inHg. The twist is 10 ÷ 0.308 = 32.47 calibres and the length 1.24 ÷ 0.308 = 4.026 calibres. Sg = 30 × 175 ÷ (32.47² × 0.308³ × 4.026 × (1 + 4.026²)) = 2.460 at 2,800 ft/s. The velocity factor (2,650 ÷ 2,800)^⅓ = 0.9818 gives Sg 2.42: fully stable, spinning at 190,800 rpm. Sg 1.5 needs 1:12.7 in or faster, a 1:12 in barrel gives 1.68 and a 1:14 in barrel gives 1.23 (marginal). In this twist, a 175 gr bullet up to about 1.46 in long would still reach Sg 1.5. Greenhill gives 150 × 0.308² ÷ 1.24 = 1:11.5 in.
Sources: Miller twist rule — Wikipedia · Courtney & Miller (2012), A Stability Formula for Plastic-Tipped Bullets, Part 1 · Berger Bullets twist rate stability calculator (inputs, altitude via ICAO atmosphere, flat-base caveat)
Frequently asked questions
What Sg do I need?
At least 1.0 to avoid tumbling. Aim for 1.4 as a practical minimum and 1.5 or more for the full published BC (Litz). Values of 1.5–2.5 are ideal for most rifles; there is little benefit above that.
Does a faster twist hurt accuracy?
Rarely in practice. The old worry about over-stabilisation mostly concerns slightly larger spin drift and thin-jacketed bullets that fail from centrifugal force. Long-range shooters choose fast twists (1:7–1:8 in .224, 1:8 in 6.5 mm) on purpose.
Where do I get the bullet length?
Manufacturers publish it, or measure it with calipers. Length matters far more than weight: a copper monolithic is longer than a lead-core bullet of the same weight and needs a faster twist. If you cannot find it, about 4.2 × the diameter is a typical starting guess for a spitzer.
Why does temperature and altitude change stability?
Sg is proportional to the inverse of air density. Cold air and high pressure are denser, so a bullet that is Sg 1.5 at 59 °F drops to about 1.33 at 0 °F. Thin air at altitude raises Sg; at 5,000 ft it is about 20% higher than at sea level.
How do I convert twist to millimetres?
Multiply the inches by 25.4: a 1:10 in twist is one turn in 254 mm and a 1:8 in twist is one turn in 203 mm. You can enter twist, diameter and length in mm with the unit selectors.
Is the Greenhill formula still useful?
For short lead and cast bullets it is a reasonable first guess. For long boat-tail match bullets it tends to suggest a twist that is too slow, so use the Miller result.
Related calculators
Sport-shooting and hunting arithmetic from standard published formulas (SAAMI energy, Miller stability, free-recoil energy). Follow all range rules and local law; verify every zero and correction on paper at the range — calculators inform, they do not replace live confirmation.