Rocket Equation Calculator

Calculate rocket performance using the Tsiolkovsky rocket equation. This equation relates the change in velocity (Δv) with the effective exhaust velocity (v_e) or specific impulse (I_sp) and the mass ratio of the rocket.

Calculation Type

Initial Mass

Final Mass

Mass Unit

Specific Impulse (I_sp)

The Rocket Equation

Δv = v_e × ln(m₀/m_f)

Also known as the Tsiolkovsky Rocket Equation

Where:

ΔvDelta-v: maximum change in velocity that the rocket can achieve
v_eEffective exhaust velocity of the propellant (v_e = I_sp × g₀)
I_spSpecific impulse of the propellant
g₀Standard gravity at Earth's surface (9.80665 m/s²)
m₀Initial total mass, including propellant
m_fFinal total mass without propellant
lnNatural logarithm

Key Concepts:

The rocket equation demonstrates that achieving higher delta-v requires either higher exhaust velocity (better propellant) or a higher mass ratio.
Mass ratio is limited by structural requirements - a rocket needs structure to hold the propellant.
Specific impulse is a measure of propellant efficiency - higher values mean more efficient propellant.
For chemical rockets, typical specific impulse values range from ~250-450 seconds.
For ion/electric propulsion, specific impulse can exceed 3000 seconds.

Multi-stage Rockets

Multi-stage rockets improve delta-v by discarding empty tanks and engines as propellant is used. The total delta-v of a multi-stage rocket is the sum of the delta-v of each stage.