Formula & Calculator
Specific Impulse
A measure of propulsion efficiency: thrust per unit weight flow of propellant.
Specific Impulse Calculator
Isp = F / (ṁ · g0)
Calculate the specific impulse of a rocket or jet engine.
All fields are required. Values must be positive numbers.
Interpretation
Specific impulse: I_sp = F / (ṁ·g₀), where F is thrust, ṁ is propellant mass flow rate, g₀ is standard gravity. It measures propulsion efficiency: higher I_sp means better fuel economy. Example: F=200,000 N, ṁ=50 kg/s, g₀=9.81 → I_sp = 200000/(50×9.81) ≈ 408 s.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| I_sp | Specific impulse | s |
| F | Thrust | N |
| ṁ | Mass flow rate | kg/s |
| g₀ | Standard gravity | m/s² |
What it means
Specific impulse (I_sp) is a key performance metric for rockets and jet engines, indicating how effectively the propellant is converted into thrust. It is defined as the thrust per unit weight flow rate of propellant, with units of seconds. The higher the I_sp, the less propellant is needed to achieve a given Δv, which is critical for spacecraft mass fraction. For chemical rockets, I_sp typically ranges from 250‑450 s; for ion thrusters, it can exceed 3000 s. The formula shows that I_sp is proportional to the effective exhaust velocity (v_e/g₀). It is used in the Tsiolkovsky rocket equation to determine mass ratios and in mission planning to compare propulsive options. In aircraft, it relates to thrust specific fuel consumption (TSFC). Understanding I_sp is essential for aerospace engineers to optimise propulsion system design and mission feasibility.
Worked example
Specific Impulse – Two Examples
Real‑World| Parameter | Value |
|---|---|
| F | 250,000 N |
| ṁ | 85 kg/s |
| Parameter | Value |
|---|---|
| F | 450,000 N |
| ṁ | 140 kg/s |
Common mistakes
- Specific impulse I_sp: Usually in seconds – I_sp = F / (ṁ·g₀).
- g₀: Standard gravity (9.80665 m/s²) – not local g.
- Units: F in N, ṁ in kg/s → I_sp in seconds.
- Higher I_sp: Indicates better propellant efficiency; typical values: 250‑450 s for chemical rockets.
- Effective exhaust velocity: v_e = I_sp·g₀ – often used in rocket equations.
Applications
Specific impulse, I_sp = F / (ṁ·g₀), is a measure of rocket engine efficiency, representing the thrust per unit weight flow of propellant (with units of seconds). Higher I_sp indicates better fuel efficiency, allowing rockets to achieve higher delta‑v for a given propellant mass. This figure of merit is essential for comparing propellant combinations (e.g., hydrazine vs. hydrogen‑oxygen) and for preliminary design of launch vehicles and upper stages. Engineers use I_sp to compute propellant mass fractions, to size fuel tanks, and to optimise engine parameters. In electric propulsion (ion thrusters), I_sp can be very high, enabling long‑duration missions. By understanding specific impulse, aerospace engineers can make informed choices about propulsion systems, balancing performance, cost, and safety.
- Propellant selection and performance comparison
- Launch vehicle preliminary design and mass budgeting
- Engine cycle trade‑off studies (chemical, electric, nuclear)
- Propulsion system optimisation for interplanetary missions
- Education and standardisation of rocket engine metrics
Frequently Asked Questions
Specific impulse (Isp) is a measure of propulsion efficiency: thrust per unit weight flow of propellant. It is the rocket engine equivalent of fuel economy.
In SI, Isp is expressed in seconds (s) when using g0 = 9.81 m/s². It can also be given as effective exhaust velocity (m/s) = Isp × g0.
Because F/(ṁ·g0) has dimensions of (kg·m/s²)/(kg/s · m/s²) = seconds. This convention is widely used in rocketry.
- Solid rockets: 250–300 s
- Liquid hydrogen/oxygen: ~450 s (vacuum)
- Kerolox (RP‑1/LOX): ~350 s
Effective exhaust velocity ve = Isp × g0. Higher Isp gives faster exhaust, increasing thrust for a given mass flow.
Δv = Isp · g0 · ln(minitial/mfinal). A higher Isp yields a larger Δv for the same mass ratio.
Chemical energy content of propellants, nozzle efficiency, and thermodynamic constraints. Nuclear or electric propulsion can achieve much higher Isp (up to thousands of seconds).
Measure thrust (F) and mass flow rate (ṁ) on a test stand, then compute Isp = F/(ṁ·g0). Corrections for ambient pressure may be applied.
Specific impulse is per unit propellant weight flow. Total impulse (It = ∫F dt) is the total momentum delivered, and it scales with propellant mass.
A rocket engine produces F = 100 kN at ṁ = 25 kg/s. Compute Isp:
Isp = 100000 / (25×9.81) = 100000 / 245.25 ≈ 407.8 s.