# Specific Impulse Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Jan 13, 2022

This specific impulse calculator will help you estimate the performance of a jet or rocket engine. Specific impulse is often used to find out how well the engine is producing thrust . This parameter is vital to compare the performance of engines of different classes, as it is only a function of thrust generated and exhaust velocity or mass flow rate.

An engine with a higher specific impulse value is more efficient as it produces more thrust per mass of fuel or propellant. It also varies based on the function and type of engine; for instance, the specific impulse of a rocket engine is much lower than that of a jet engine.

The specific impulse equation helps in the initial analysis to estimate a rough size for the engine and how much mass flow rate of fuel is needed. So, what is a specific impulse? Read on to understand the specific impulse formula and its usage.

## What is specific impulse?

Specific impulse is the time an engine can generate thrust force equal to its mass at 1g. In other words, it is the impulse produced by the engine per unit mass of propellant. The specific impulse is directly proportional to the thrust and inversely proportional to the mass flow rate. It dictates the propellant flow rate required to achieve the thrust equal to its mass for the said duration or vice versa. Consider an engine producing thrust $F$ over time $dt$, the total impulse is given by:

$\quad I = \int F \,dt$

We measure specific impulses in units of time, i.e., seconds. That makes this parameter a convenient way to compare performance across different engines. The specific impulse shows how efficiently propellant is used. A higher specific impulse value implies a rocket will climb higher altitude efficiently.

## Specific impulse formula

The specific impulse equation for an engine producing thrust, $F$, with mass flow rate $\dot m$ is:

$\quad I_{sp} = \frac{F}{\dot{m}g_0}$

If you don't know the thrust produced by the engine having dry weight, $W$, you can use the thrust-to-weight ratio $T_r$, to estimate it, which is:

$\quad T_{r} = \frac{F}{W} \implies I_{sp} = \frac{WT_r}{\dot{m}g_0}$

However, the thrust $F$ is also related to exhaust velocity $v_e$ as:

$\quad F = \dot{m} v_e \implies I_{sp} = \frac{v_e}{g_0}$

Thrust-specific fuel consumption (TSFC): The fuel efficiency of an engine. Basically, the mass of fuel consumed per unit time to achieve unit thrust. The term thrust-specific means this parameter can be called fuel consumption with respect to unit thrust. It is measured in the units grams of fuel per second-kilonewtons of thrust, $\text{g/(s}\cdot\text{kN)}$ or pounds of fuel per hour-pound of thrust $\text{lb/(h}\cdot\text{lbf)}$ in imperial units. Mathematically, this is:

$\quad\text{TSFC} = \frac{\dot m}{F}$

An inverse of the TSFC parameter is called specific thrust, i.e., the thrust produced per unit flow rate of fuel. The specific thrust $F_s$ is equal to:

$\quad F_s = \frac{F}{\dot m}$

## How to calculate specific impulse

The calculator has technical data for some engines that you can directly use. If your configuration is not on the list, please use the Custom option to input the data.

To calculate specific impulse:

1. Enter the thrust produced by the engine.
2. Fill in the exhaust velocity.
3. The calculator will return:
• Specific impulse, $I_{sp}$; and
• Thrust-specific fuel consumption (TSFC).

💡 You can use the advanced mode to adjust the gravitational acceleration, or you wish to use the thrust-to-weight ratio-based input.

## Example: Using the specific impulse calculator

Determine the specific impulse of an engine delivering 8000 N of thrust and having exhaust velocity of 20000 m/s.

1. Enter the thrust, $F = 8000 \text{ N}$
2. Fill in the exhaust velocity, $v_e = 20000 \text{ m/s}$.
3. Using the specific impulse equation:
$\quad \ \ \ \small I_{sp} = \frac{v_e}{g_0} = \frac{20000}{9.80665} = 2070 \text{ s}$

## FAQ

### What do you mean by specific impulse?

Specific impulse is the parameter that tells us for how many seconds the engine would produce one pound of thrust using one pound of propellant or fuel. In other words, the specific impulse is a measure of how long an engine can continuously generate thrust by completely burning a unit mass of fuel. Continuous thrust implies an acceleration of the body attached to the engine.

### How do I calculate specific impulse?

To calculate the specific impulse of an engine:

1. Find the thrust produced by the engine.
2. Divide the thrust with the mass flow rate.
3. Divide the resultant with gravitational acceleration to obtain the specific impulse.

Alternatively:

1. Divide the exhaust velocity with gravitational acceleration to obtain the specific impulse.

### What is the unit of specific impulse?

The unit of specific impulse is seconds. The specific impulse formula is Isp = F / (ṁ × g), the unit of Isp = 1 N/((kg/s) × (m/s²)) = 1 N/(kg⋅m/s³). But since 1 N = kg⋅m/s², the units of specific impulse becomes (1 kg⋅m/s²) / (kg⋅m/s³) = s.

### What is thrust-specific fuel consumption?

It is the fuel consumption in mass per second to produce unit thrust output. This parameter is also considered as the fuel efficiency of the engine. Mathematically, it is the ratio of mass flow rate and thrust produced and has the units of g/(s⋅kN) or lb/(h⋅lbf).

Rahul Dhari
Engine specifications
Engine
General Electric GE F404
Thrust (F)
lbf
Propulsion properties
Mass flow rate (ṁ)
lb/s
Exhaust velocity (Ve)
ft/s
Performance parameters
Specific impulse (Isp)
sec
Thrust-specific fuel consumption (TSFC)
lb/(h·lbf)
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