# Recoil Energy Calculator

Created by Krishna Nelaturu
Last updated: Nov 21, 2022

Our recoil energy calculator will help you analyze a firearm's recoil energy and recoil impulse. Understanding recoil is crucial in most weapons, from handguns to artillery. In this article, we shall briefly look at some basics of recoil energy, including:

• What is recoil energy?
• Formula for recoil energy.
• Calculating free recoil energy.

We also have a tool called projectile range calculator that finds the launch distance of thrown projectiles. Check it out if you're interested!

## Recoil energy and recoil impulse

Anyone who has ever fired a gun can attest that the experience is not just about noise and smoke. There is also a notable amount of recoil or rearward movement of the gun as it propels the bullet forward. Recoil energy is the kinetic energy of this backward thrust/movement.

It may seem like a simple matter of physics, but in fact, the recoil energy of a firearm can be pretty complex. Factors like the weight and size of the weapon, the type of ammunition, and even the weather conditions at the time of firing can influence the recoil of a firearm. Understanding recoil energy is essential for anyone who wants to use a gun safely and effectively.

Free recoil is the recoil of a weapon where it is allowed free motion during recoil - meaning there is no support or obstruction to counteract the recoil. Our recoil calculator calculates free recoil energy.

## Formula for recoil, recoil energy and recoil impulse

The formula for the recoil velocity is:

$V_f = \frac{M_b \cdot V_b + M_c \cdot V_c}{1000 \cdot M_f}$

Where:

• $V_f$ - Recoil velocity of the firearm in meters per second;
• $M_b$ - Mass of the bullet in grams;
• $V_b$ - Velocity of the bullet in meters per second;
• $M_c$ - Mass of the powder charge in grams;
• $V_c$ - Velocity of the powder charge in meters per second; and
• $M_f$ - Mass of the firearm in kilograms.

The following table lists some averaged values of powder charge velocity $V_c$ for different firearms:

Powder for

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

Handguns and Shotguns

1707 [5600]

Rifles

1585 [5200]

BMGs

1433 [4700]

Black powder

685.8 [2250]

Once we calculate the recoil velocity, we can use it to find the recoil energy. The formula for recoil energy is:

$E_r = \frac{1}{2} M_f \cdot V_f^2$

Where $E_r$ is the recoil energy of the firearm in Joules. Notice that recoil energy is the same as kinetic energy.

The recoil impulse is the impulse at the moment of firearm recoil. Considering the initial velocity of the firearm is zero, we can derive an equation for the recoil impulse:

$I_r = M_f \cdot (V_f - 0) = M_f \cdot V_f$

## How to use this recoil energy calculator

Our recoil energy calculator is simple to use:

1. Enter all of the following data, taking care of the units used:
• Mass of the bullet in grams;
• Velocity of the bullet;
• Mass of the powder charge in grams;
• Velocity of the powder charge; and
• Mass of the firearm in kilograms.
2. The recoil energy calculator will use these values to determine the following outputs:
• Recoil velocity of the firearm;
• Recoil energy of the firearm; and
• Recoil impulse of the firearm.
Krishna Nelaturu
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
Recoil velocity of firearm (Vf)
ft/s
Recoil properties
Recoil energy (Er)
J
Recoil impulse (I)
lbf⋅s
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