⦿ JOSEF'S STABILITY CALCULATOR

References:
Miller, D.G. (2005). A New Rule for Estimating Rifling Twist. Precision Shooting.
Miller, D.G. (2009). How Good Are Simple Rules for Estimating Rifle Twist. Precision Shooting.
Courtney, M. & Miller, D.G. (2012). A Stability Formula for Plastic-Tipped Bullets. Precision Shooting.
Litz, B. Modern Advancements in Long Range Shooting, Vol. I. Applied Ballistics (live-fire tests of BC vs. stability).
Checked against JBM Stability Calculator (online calculators retired in 2026): Sg 1.378 at standard conditions for a .308 165 gr bullet, 33 mm, 2625 fps, 1:12″ (this page: 1.378). The atmospheric correction was checked against the Berger Twist Rate Calculator and QuickTARGET for the same bullet (33.1 mm, 800 m/s): Sg 1.38 at 15 °C / sea level, 1.21 at −20 °C and 1.75 at 2000 m — the same ratios as this page's linear correction.

* The atmospheric correction is linear in the air-density ratio, as in Miller's original rule (P_std/P · T/T_std). Versions up to v2.0.2 used the square root of this factor — see [7].

[1] Polymer-tip bullets and Miller conservatism: Miller's stability formula uses total bullet length to estimate the aerodynamic overturning moment (C_Mα). For bullets with a low-density polymer tip (e.g. Hornady InterBond, ELD-X, Nosler AccuBond), the tip contributes to geometric length but adds negligible mass, leaving the centre of mass further rearward than geometry alone suggests. This causes Miller to overestimate C_Mα and therefore overestimate the twist rate required for stability — meaning calculated S_g may be conservatively low for these designs. In the examples published by Courtney & Miller (2012) the effect is about 31–41 % on S_g.

Courtney & Miller (2012, Precision Shooting) published a correction: substitute only the metal portion length (total length minus tip) in the (1+l²) moment-of-inertia term, while retaining total length elsewhere. This calculator implements that correction automatically — enter total bullet length and the polymer tip length separately, and the app subtracts the tip to compute the effective metal length. Leaving the tip field at 0 uses the standard Miller formula with full bullet length — a conservative estimate suitable when the tip length is unknown.

Hornady's 4DOF calculator accounts for tip geometry through measured per-bullet aerodynamic coefficients; Miller-based tools apply the Courtney correction as a practical approximation. If a polymer-tip bullet shows a low S_g (below 1.5) under standard Miller but performs stably at the range, entering the measured tip length will typically bring the calculated value into agreement with observed behaviour.

[2] G1→G7 conversion factor (1.98): The Litz (2009) factors commonly cited in literature (1.43–1.60 by bullet type) were derived from early live-fire chronograph data and do not reflect modern radar-based measurements. Manufacturer-published G1/G7 BC pairs show a consistent G1/G7 ratio of approximately 1.95–2.00 across pointed boattail constructions:
SourceTypeRatio (mean ± std) Berger (n=8)mixed BT types1.951 ± 0.003 Nosler AccuBond LR (n=13)VLD BT hunting1.986 ± 0.003 Lapua Scenar (n=5)HPBT/OTM1.998 ± 0.005 Hornady ELD-X/M (n=6)Polymer tip BT1.975 ± 0.014
The factor 1.98 is the weighted mean of these 32 bullets. Versions up to v2.0.2 used 1.95, described as a conservative lower bound; it is not conservative — a smaller divisor gives a larger G7 BC, i.e. less drag and an optimistic result. Provenance: the Berger and Nosler values were transcribed from the manufacturers' pages; the Lapua and Hornady values were taken from the manufacturers' websites without recorded page addresses. For best accuracy, enter a measured G7 BC directly — the estimator is a fallback when only G1 is known.

[3] Flat-base correction (twist × 1.15, Sg × 1.32): Miller's denominator (1 + lc²) is empirically calibrated for boat-tail bullet geometry. For flat-base bullets, the aerodynamic overturning moment (C_Mα) is lower, meaning actual gyroscopic stability is higher than Miller predicts. To derive a correction, Miller's twist for S_g = 1.5 (2800 fps, standard atmosphere) was compared with Berger Bullets' published minimum twist rates for 13 flat-base bullets (.17 to .30 caliber). Berger allows a slower twist than Miller for every bullet: the twist ratios (Berger T / Miller T) range from 1.10 to 1.29 (mean 1.21, std 0.057, n = 13). A twist factor of 1.15 (mean − 1σ) is applied, so the correction stays conservative for about 84 % of the dataset. Because S_g scales with 1/T², the corresponding S_g factor is 1.15² ≈ 1.32. Versions up to v2.0.2 applied 1.15 directly to S_g (equivalent to only a 1.07× twist factor, smaller than any bullet in the dataset); this was corrected in v2.1. The corrected S_g is used for the zone, BC degradation, transonic distance and spin drift. Provenance and limits: the Berger twist values survive as a transcription of Berger's published table, and the bullet lengths come from web sources without recorded page addresses; the calibration was recomputed for v2.1 and reproduces the original statistics. This correction is derived from flat-base data only. Round-nose bullets share the absence of a boat tail but have a fundamentally different nose geometry that shifts the center of pressure forward, potentially increasing C_Mα relative to flat-base designs. In the absence of comparable empirical data for round-nose bullets, the correction factor cannot be reliably extended to that geometry — manufacturer twist rate recommendations should be consulted instead.

[4] Stability zones and BC degradation: True gyroscopic instability and tumbling occur only below S_g = 1.0. Between 1.0 and 1.5 the bullet flies point-forward, but its ballistic coefficient degrades measurably, as the bullet's coning motion (precession and nutation) increases aerodynamic drag. Live-fire tests by Litz (Applied Ballistics) show BC essentially constant above S_g = 1.5 and a loss of about 3 % per 0.1 below it, which is the degradation model used here. The zones are therefore: below 1.0 unstable (tumbles; BC, transonic distance and spin drift are not shown); 1.0–1.3 marginal (significant BC loss, precision may suffer); 1.3–1.5 acceptable (some BC loss); 1.5–2.0 stable (full BC); above 2.0 very stable. The minimum twist is computed for S_g = 1.3 and the stable twist for S_g = 1.5. For the most accurate trajectory predictions, use the effective BC shown in the results rather than the manufacturer's nominal BC when entering data into an external ballistics calculator.

[5] Very stable (Sg ≥ 2.0): Whether high Sg causes practical problems is debated. Lapua and traditional sources recommend keeping Sg below 2.0, citing increased drag from nose-up flight and sensitivity to bullet imperfections. Berger/Litz counter that Doppler radar data shows higher Sg actually reduces drag, especially in the transonic region — the nose-up myth originates from high-angle artillery fire, not small arms ballistics. In practice, Sg 1.4–2.0 is the broadly agreed optimal window. Values above 2.0 are generally still accurate but represent an unnecessarily fast twist for the bullet used.

[6] Transonic distance: Calculated using a point-mass drag model with Gehtsoft/BRL C_d(M) tables — G7 (84 points) or G1 (79 points) — and π/8 (Siacci/Ingalls) normalization, with no empirical correction factors. The model integrates velocity loss in 1 ms steps using actual atmospheric conditions. The G7 model is used whenever a G7 BC is available: either entered directly or, for pointed boat-tail bullets, estimated from G1 (BC_G1/1.98, see [2]); the result is then marked “G7 est.”. The G1 model is used only for flat-base and round-nose bullets without an entered G7 BC. The effective (stability-corrected) BC is used, so marginal stability (S_g < 1.5) also shortens the transonic distance. The transonic distance is the distance to Mach 1.2 (~408 m/s at ISA) — the onset of the transonic region. It is not shown when S_g < 1.0. Miller's formula assumes the aerodynamic pitching moment scales predictably with velocity, but this assumption breaks down as drag rises rapidly and non-linearly through the transonic region. While Miller produces numerical output down to Mach 1.0 and below, its predictive value degrades progressively from Mach ≈ 1.2. Beyond this range actual stability depends on dynamic stability (S_d) — factors not modelled here.

[7] Atmospheric correction and humidity: S_g is inversely proportional to air density, because the aerodynamic overturning moment scales linearly with density. The correction is therefore linear in the density ratio, f_atm = (P_std/P) · (T/T_std), relative to the ICAO standard atmosphere (15 °C, 1013.25 hPa, dry air) — the form used in Miller's original rule (2005) and in Courtney & Miller (2012). Versions up to v2.0.2 applied the square root of this factor, in the belief that it agreed better with JBM and Berger; those comparisons had been made only near standard conditions, where both forms give identical results. A test at −20 °C showed that Berger's Twist Rate Calculator and QuickTARGET both use the linear form (a .308 165 gr bullet in a 1:12″ twist drops from S_g 1.38 to 1.21). The square-root form had overstated S_g in cold air (by about 7 % at −20 °C and 9 % at −30 °C) and understated it at low pressure (by about 8 % at 850 hPa, roughly 1500 m altitude, and 17 % at 700 hPa); at standard conditions, results are unchanged. Humidity is not included: the standard atmosphere is defined for dry air, and 0 → 100 % RH at 15 °C lowers density by about 0.6 %, raising S_g by about 0.6 % (≈ 0.01) — below the precision of the inputs. For trajectory-level humidity handling (Tetens saturation vapour pressure), see the companion External Ballistics calculator.