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    Rocketry

    Rocket Equation (Delta-v) Calculator

    Tsiolkovsky rocket equation: delta-v from specific impulse and wet/dry mass.

    Δv = Isp · g₀ · ln(m₀ / m_f)

    Inputs

    s

    Results

    Delta-v
    4.90857 km/s
    Effective exhaust velocity
    3.04987 km/s
    Mass ratio m₀/m_f
    5
    Propellant fraction
    80 %
    Worked solution
    1. vₑ = Isp × g₀ = 311 × 9.80665 = 3,049.9 m/s
    2. ln(m₀/m_f) = ln(5) = 1.60944
    3. Δv = 3,049.9 × 1.60944 = 4,908.6 m/s

    How the result changes

    Delta-v (km/s) plotted against Final mass (tonnes), from one quarter to four times your input, with your input marked.246820406080Final mass (tonnes)Delta-v (km/s)your input
    Delta-v vs final mass

    How it works

    Konstantin Tsiolkovsky showed in 1903 that a rocket's velocity change depends only on its exhaust velocity and the logarithm of its mass ratio. Because of the logarithm, adding more propellant gives diminishing returns, which is why large rockets use stages.

    Reaching low Earth orbit takes about 9.3–10 km/s of Δv in practice: about 7.8 km/s orbital speed plus gravity and drag losses.

    Variables

    • Δv — change in velocity the stage can deliver
    • Isp — specific impulse (seconds)
    • g₀ — standard gravity, 9.80665 m/s²
    • m₀, m_f — initial (wet) and final (dry) mass

    Assumptions and limits

    • Single stage, constant specific impulse
    • No gravity losses, drag or steering losses (ideal Δv)
    • Thrust acts along the direction of motion

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.