# Twist Rate Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Feb 02, 2023

The twist rate calculator will assist you in determining the stability of a bullet when fired from a particular rifled barrel. It has been long-established that in order for a bullet to travel long distances while maintaining stability, the bullet should spin or rotate along the longitudinal axis. This spin on a bullet is induced by introducing grooves in the barrel. The bullet stability is varied with different barrels and is estimated using the Greenhill formula or the Miller twist rule. Read on to understand what is twist rate and how to calculate twist rate?

## What is twist rate?

The most common part of a firearm is the barrel. From the early 17th and 18th-century's muzzle-loaded muskets having an effective combat range of a few hundred yards to the modern Barrett M82 which has a maximum range of about 1900 yards, the accuracy and range of firearms have come a long way. Not just for handheld firearms, this leap in technology has also benefitted artillery guns, modern howitzers have a combat range about 20 times the artillery guns used during the American Civil War.

Much of it is attributed to different shapes of bullets conforming to aerodynamics, to avoid tumbling midair and achieve greater stability. The bullet stability has been improved by inducing the spin to the bullet, along its longitudinal axis, to ensure higher time of flight and range. The spin is achieved by the means of torque exerted by grooves inside the barrel.

However, there are still artillery and tank guns without grooves, i.e., the smoothbores. These guns are specialized to fire kinetic energy projectiles which are too long compared to their diameter. Such projectiles are stabilized using specialized fins. The smoothbore barrels have less wear and tear and therefore have a longer life.

Projectile motion
Visit projectile range calculator, time of flight calculator, and projectile motion calculator for basics on the trajectory of a projectile.

The process of having grooves in a barrel is known as rifling. It is specified in terms of twist rate. This twist rate is defined as the distance traveled by a bullet to complete one full revolution. A barrel twist rate is measured as 1:x inches, i.e., 1 turn in x inches or alternatively x inches per turn in English units or 1 turn in y mm in SI units. There are two popular formulae to calculate the required rifle twist rate and bullet stability.

• Greenhill's formula
• Miller twist rate

Greenhill formula: Introduced in 1879 by Prof. George Greenhill, is still used as a rule of thumb to estimate the twist rate t in inches per mm using the equation:

$t = \frac{C~D^2}{L} \sqrt{\frac{\mathrm{SG}}{10.9}}$

where:

• C — A constant, whose value is 150 or 180 (if the muzzle velocity is greater than 2800 ft/s);
• D — Diameter of bullet/projectile in inches;
• L — Length of projectile in inches; and
• SG — Specific gravity (see specific gravity calculator).

Miller twist rule: The rule uses a semi-empirical relation to estimating the stability of the bullet. The dimensionless gyroscopic stability factor s for a bullet having mass m and dimensional parameters, as diameter D and length L is:

$s = \frac{30~m}{t^2 D^3 l (1 + l^2)}$

Similarly, the equation for uncorrected twist t, given as twist per one caliber, is achieved by rearranging the terms:

$t^2 = \frac{30~m}{s D^3 l (1 + l^2)}$

Initially, the value of s is used as 2.0 which is known as the safe value for the stability factor. The twist rate, in inches per turn T can be found out by multiplying the twist t from the Miller twist rule with the diameter of the bullet. This calculator directly provides you the value of T.

$T = t\times D$

The Miller twist rule is valid for the parameters in the English units, such that:

• Mass of bullet, m is in grains;
• Length of bullet, L is in inches; and
• Diameter of bullet, D is in inches.

## Correction factors for Miller twist rule

The above formulae for rifle twist rate do not account for conditions such as temperature, atmospheric pressure, and altitude. The change in conditions results in a change in the stability factor and therefore the need to change the barrel having a different twist rate or the bullet. There's also a need to make corrections to the formula based on the muzzle velocity. These conditions are reported to cause an effect on the bullet stability by 20% or even higher.

Velocity correction: For a bullet projectile having muzzle velocity of more than 2800 ft/s (~853 m/s), the correction factor $f_\mathrm{v}$ can be calculated as:

$f_v = \left [ \frac{v}{2800} \right ]^{0.33}$

The square root of the above correction factor is multiplied by the twist t obtained from the Miller twist rule, to obtain the corrected twist for the muzzle velocity. Such that:

$t = t_{2800} \left [ \frac{v}{2800} \right ]^{1/6}$

Similarly, the correction factor is directly related to the gyroscopic stability factor s as:

$s = s_{2800} \left [ \frac{v}{2800} \right ]^{1/3}$

Altitude correction factor: This factor is used to account for the high or low altitude. The correction factor is the function of altitude or height in feet above sea level:

$f_\mathrm{h} = e^\mathrm{3.158 \times 10^{-5} h}$

The square root of the above factor is multiplied directly with the stability factor s and twist t to obtain the corrected values.

Temperature correction factor: The change in temperature results in pressure and density, causing the bullet to behave differently midair. The equation to factor in the temperature is:

$\scriptsize f_t = \frac{ P_\mathrm{std} } {P_\mathrm{T} } \frac{T_\mathrm{F} + 460}{460 + 59}= \frac{ P_\mathrm{std} } {P_\mathrm{T} } \frac{T_\mathrm{C} + 273}{273 + 15}$

where $P_\mathrm{std}$ and $P_\mathrm{T}$ are standard and current atmospheric pressures. $T_\mathrm{C}$ and $T_\mathrm{F}$ are temperature in Fahrenheit and Celsius scale, respectively. Similar to the altitude correction factor, the square root of the above factor is multiplied by the uncorrected twist t and stability factor s to obtain the corrected result.

## How to calculate twist rate?

To calculate twist rate using the Miller twist rule:

1. Select the formula you wish to use – Miller twist rule.
2. Enter the mass of bullet projectile, m.
3. Input the diameter (caliber) of bullet, D.
4. Fill in the length of bullet, l.
5. Use the safe value of gyroscopic stability factor as 2.
6. The twist rate calculator will return the value of uncorrected twist in inches per turn.

If you wish to obtain the corrected values for twist and stability factor:

1. Enter the temperature.
2. Insert the atmospheric pressure.
3. Fill in the altitude, if necessary.
4. The calculator will use the above equations to return the correction factors and the corrected values.

To calculate twist rate using Greenhill formula:

1. Input the diameter of bullet, D.
2. Fill in the length of bullet, l.
3. The calculator will return the value of the required twist, in inches per turn.

## Example: Using the twist rate calculator

Find the appropriate twist rate using the Miller twist rule for a 168 gr bullet having a diameter of 0.308 in and length as 3.98 in. Take the stability factor s as 1.8.

To calculate twist rate using Miller twist rule:

1. Enter the mass of bullet projectile, m = 168 grains.
2. Input the diameter of bullet, D = 0.308 in.
3. Fill in the length of bullet, l = 3.98 in.
4. Use the value of gyroscopic stability factor as 1.8.
5. Using the bullet stability calculator:
\scriptsize \qquad \begin{align*} t^2 &= \frac{30 \times 168}{1.8 \times 0.308^3 \times 3.98 (1 + 3.98^2)}\\ &= 1429.8 \end{align*}
1. The twist rate in inches per turn is
$\scriptsize \qquad 1429.8^{0.5} \times 0.308 = 11.646~\mathrm{in./turn}.$

## Gyroscopic stability factor – bullet stability calculator

The value of the gyroscopic stability factor is used to determine if the bullet is stable or not. For a projectile, the stability factor is measured as:

Stability range

Property

<1

Unstable

1-1.5

Marginally stable

1.5

## FAQ

### What is twist rate?

The distance a projectile travels to complete one full revolution along its longitudinal axis is known as twist rate. It is measured as inches or mm per turn.

### How do I calculate twist rate using Greenhill formula?

To calculate twist rate using Greenhill's formula:

1. Divide the specific gravity, SG of the bullet by 10.9.
2. Find the square root of the resultant.
3. Multiply the resultant with constant C, 150, and the square of the projectile diameter, D.
4. Divide the product by the length of the projectile L to get the twist rate in inches per turn, t.

t = C * D²/ L * √(SG/10.9)

### What is the velocity correction factor for the Miller twist rule?

The velocity correction factor is f_v = (v/2800)^0.33.
It is used to take the higher muzzle velocity cases into account. The formulation is valid for muzzle velocity greater than 2800 ft/s.

### How to calculate temperature correction factor for Miller twist rule?

To calculate temperature correction factor in Fahrenheit scale:

1. Add 460 to the temperature (in Fahrenheit).
2. Divide the sum by 519.
3. Multiply the resultant with standard atmospheric pressure.
4. Divide the product with current atmospheric pressure.
Rahul Dhari
Formula
Miller twist rule
Bullet parameters
Mass (m)
gr
Diameter (caliber) (d)
in
Length (l)
in
Muzzle velocity (V)
ft/s
Gyroscopic stability factor (s)
Uncorrected twist rate
Twist
in
/ turn
Conditions
Temperature (T)
°F
Pressure (Pₜ)
psi
Height (h)
ft
Correction factors
Temperature correction factor (fₜ)
Altitude correction factor (fₕ)
Velocity correction factor (fᵥ)
Corrected parameters
Correction
Velocity
Gyroscopic stability factor (sᵥ)
Twist (tᵥ)
in
/ turn
Corrected for Velocity, Temperature, and Height
Gyroscopic stability factor
Twist
in
/ turn
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