# Recoil Energy Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Dec 21, 2022

This recoil energy calculator estimates the impulse and energy of the free recoil from discharging a firearm. From handguns to cannons, the amount of recoil energy dissipated remains a crucial parameter as it moves the weapon from its primary firing position or stance.

The recoil energy and impulse can also affect the accuracy and precision of shooting continuous ammunition. The parameter, free recoil, depends on several factors such as the weight of the firearm, properties of the projectile, and the powder charge used. Read on to understand recoil energy and using the free recoil energy calculator.

## Definition of recoil energy

When a weapon or firearm is discharged, the ignited powder results in the release of high-velocity gases, which then propels the projectile forward. Find more on projectile motion using our projectile motion calculator. This reaction follows Newton's third law, such that the weapon imparts an equal reaction towards the shooter in the backward direction.

This reaction varies for different firearms and is known as recoil. The energy associated with this reaction is the translational kinetic energy of the firearm. This kinetic energy is known as recoil energy. It is measured in joules (J) or foot pounds-force (ft-lbf).

Remember that this recoil energy is not potential energy. For more details on the differences between various types of energy, check the potential energy calculator and kinetic energy calculator. You can also explore ballistic coefficient calculator that explains about the stability of bullets.

Consider a firearm, having mass $M_\mathrm{f}$, firing a bullet of mass $M_\mathrm{b}$. The velocity $V_\mathrm{f}$ with which the firearm recoils backward is related to the mass of firearm and bullet is given by the equation:

$V_\mathrm{f} = \frac{M_\mathrm{b} \times V_\mathrm{b} + M_\mathrm{c} \times V_\mathrm{c} }{1000M_f}$

where $V_\mathrm{b}$, $V_\mathrm{c}$, and $M_\mathrm{c}$ are the velocity of bullet, velocity of powder charge, and mass of powder charge respectively. The velocity of powder charge varies as per the type of propellant used, however, there is a which can be used depending on the firearm:

Powder for

Velocity (in m/s)[ft/s]

Handguns and Shotguns

1707 [5600]

Rifles

1585 [5200]

BMGs

1433 [4700]

Black powder

685.8 [2250]

Further, we calculate the kinetic energy of the firearm using the equation:

$E_r = 0.5 M_\mathrm{f} \times V_\mathrm{f}^2$

The above method is called the long-form of momentum equation. It is to be noted that the mass of bullet and powder charge is input in grams, whereas the mass of firearm is taken in kilograms and adjusted with the 1000 in the denominator.

Similarly, the velocities are in m/s. The recoil impulse $I_\mathrm{r}$ can be calculated as the product of mass and velocity of the firearm, i.e.,:

$I_r = M_\mathrm{f} \times V_\mathrm{f}$

## How to calculate recoil energy?

To calculate the recoil energy:

1. Enter the mass of bullet, $M_\mathrm{b}$.
2. Insert the velocity of bullet, $V_\mathrm{b}$.
3. Fill in the mass of powder charge, $M_\mathrm{c}$.
4. Enter the velocity of powder charge, $V_\mathrm{c}$.
5. Enter the mass of firearm, $M_\mathrm{f}$.
6. The free recoil calculator will return the velocity of firearm, $V_\mathrm{f}$.
7. The velocity of firearm is then used to calculate recoil energy $E_\mathrm{r}$ and impulse $I_\mathrm{r}$.

Note: There's a list that contains popular weapons and their respective chambered bullets that can be selected using the configuration option, e.g., AK-74 with 5.45x39 mm cartridge.

## Using the recoil energy calculator

Find the recoil energy from firing a 7.62x51 mm round from an M14 rifle. Use the following properties:

• Mass of bullet, $M_\mathrm{b} = 10.1~\mathrm{g}$.
• Velocity of bullet, $V_\mathrm{b} = 845~\mathrm{m/s}$.
• Mass of charge, $M_\mathrm{c} = 3.1~\mathrm{g}$.
• Velocity of powder charge, $V_\mathrm{c} = 1574.8~\mathrm{m/s}$.
• Mass of firearm, $M_\mathrm{f} = 4.5~\mathrm{kg}$.

This condition is available in the list, and therefore, you can obtain the answer by using the Configuration option and selecting M14 w/ 7.62x51 mm. Or you can manually insert the numbers using the steps mentioned above.

The velocity of firearm $V_\mathrm{f}$ can be found out using the formula:

\scriptsize \begin{align*} V_\mathrm{f} &= \frac{10.1 \times 845 + 3.1 \times 1574.8}{4.5 \times 10^3} \\ &= 2.98~\mathrm{m/s} \end{align*}

This implies the weapon will kick back at a velocity of 2.98 m/s, and the energy of:

$E_\mathrm{r} = 0.5 \times 4.5 \times 2.98^2 = 20~\mathrm{J}$

The recoil impulse is estimated as:

$I_\mathrm{r} = 4.5 \times 2.98 = 13.416~\mathrm{N·s}$

## FAQ

### What is recoil energy?

The energy corresponding to the kickback of a weapon when discharged, known as recoil energy. It is also known as the translational kinetic energy of the firearm.

### How do I calculate recoil energy?

To calculate recoil energy:

1. Obtain the momentum of the bullet by multiplying the mass and velocity of the projectile fired.
2. Find the product of mass and velocity of the powder charge.
3. Add both the resultants and divide them with the mass of the firearm in grams to get velocity of the firearm.
4. Find the square of the velocity of the firearm.
5. Multiply the resultant with the mass of the firearm and divide it by 2 to obtain the recoil energy.

### What is the recoil energy associated with an AKM rifle?

The recoil energy associated with an AKM rifle is 7.19 J. Such that:
Velocity of firearm: Vf = (7.9 * 710 + 1.55 * 1119) / (3.75 * 1000) = 1.96 m/s. Therefore, the energy is: Er = 0.5 * 3.75 * 1.95² = 7.19 J.

### What are the factors affecting recoil of a firearm?

The recoil of the firearm depends on the respective mass and velocities of the firearm, projectile, and powder charge.

Rahul Dhari
Configuration
Custom ▾
Projectile
Mass of bullet (Mb)
gr
Velocity of bullet (Vb)
ft/s
Powder charge
Mass of powder charge (Mc)
gr
Velocity of charge (Vc)
ft/s
Firearm
Mass of firearm (Mf)
lb
Velocity of firearm (Vf)
ft/s
Recoil properties
Recoil energy (Er)
J
Recoil impulse (I)
lbf⋅s
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