Delta-v Calculator (Tsiolkovsky Rocket Equation)
Delta-v is how much a rocket can change its speed by burning its propellant. It depends only on the engine’s specific impulse and on how much of the rocket’s starting mass is propellant.
Standards:
- NGSS HS-PS2-2
- CCSS HSF-LE.A.4
- AP1 Unit 4
- IB A.2
Our alignment; not reviewed by the standards bodies.
The equation
Worked example
- Given
- Specific impulse I_sp (s): 300 s
- Starting (wet) mass m₀ (kg): 1000 kg
- Final (dry) mass m_f (kg), less than m₀: 400 kg
- Answer
- Delta-v: 2695.7 m/s
- Mass ratio m₀/m_f: 2.500
- Propellant share of starting mass: 60.0 %
- Check
- If m₀/m_f equals e (about 2.718), the logarithm is 1 and delta-v equals I_sp × g₀ exactly; the build checks this.
Assumptions
Ideal rocket: no gravity or drag losses, constant exhaust speed. Real launches need extra delta-v for those losses.
Go deeper
Sources
- H. D. Curtis, Orbital Mechanics for Engineering Students, 4th ed., Butterworth-Heinemann (Elsevier), 2020.
- NASA, Basics of Space Flight.
- J. D. Mattingly, Elements of Propulsion: Gas Turbines and Rockets, AIAA, 2006.