# Specific Impulse Calculator

Table of contents

What is specific impulse?Specific impulse formulaHow to calculate specific impulseExample: Using the specific impulse calculatorFAQsThis 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.**

You can find more on rockets in our rocket equation calculator and rocket thrust calculator.

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:

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 altitudes efficiently.

Do you want to learn the relation between specific impulse and speed? Check our delta-$v$ calculator to dwell even deeper in spaceflight dynamics!

## Specific impulse formula

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

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:

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

**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:

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:

## 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:

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

💡 To adjust the **gravitational acceleration**, or you wish to use the **thrust-to-weight ratio-based** input, tick the "Show supplementary variables" checkbox at the bottom of the calculator.

## 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`

.

- Enter the
**thrust**, $F = 8000 \text{ N}$ - Fill in the
**exhaust velocity**, $v_e = 20000 \text{ m/s}$. - Using the specific impulse equation:

### 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:

- Find the
**thrust**produced by the engine. **Divide**the**thrust**with the**mass flow rate**.**Divide**the resultant with**gravitational acceleration**to obtain the specific impulse.

Alternatively:

**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)`

.