Rocket Delta-V Calculator Formula

Understand the math behind the rocket delta-v calculator. Each variable explained with a worked example.

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Formulas Used

Delta-V

delta_v = exhaust_velocity * log(mass_initial / mass_final)

Delta-V (km/s)

delta_v_kms = exhaust_velocity * log(mass_initial / mass_final) / 1000

Mass Ratio

mass_ratio = mass_initial / mass_final

Variables

VariableDescriptionDefault
exhaust_velocityExhaust Velocity (ve)(m/s)3000
mass_initialInitial Mass (m0)(kg)100000
mass_finalFinal Mass (mf)(kg)10000

How It Works

Rocket Delta-V (Tsiolkovsky Equation)

Delta-v is the total change in velocity a rocket can achieve by expelling all its propellant.

Formula

dv = ve * ln(m0 / mf)

  • *ve* = effective exhaust velocity
  • *m0* = initial (wet) mass
  • *mf* = final (dry) mass
  • *ln* = natural logarithm

    • The logarithmic dependence means that most of a rocket's mass must be propellant to achieve high delta-v.

    Worked Example

    ve = 3000 m/s, m0 = 100 000 kg, mf = 10 000 kg.

    exhaust_velocity = 3000mass_initial = 100000mass_final = 10000
    1. 01dv = ve * ln(m0 / mf)
    2. 02mass ratio = 100000 / 10000 = 10
    3. 03dv = 3000 * ln(10)
    4. 04dv = 3000 * 2.3026 = 6907.8 m/s

    Frequently Asked Questions

    Why is the rocket equation logarithmic?

    Because the rocket must accelerate its remaining fuel. The heavier you are, the less efficient each kilogram of fuel becomes, leading to diminishing returns.

    What delta-v is needed to reach orbit?

    Low Earth orbit requires about 9.4 km/s including gravity and drag losses. The theoretical minimum is about 7.8 km/s.

    How does staging help?

    Staging discards empty tanks, reducing dry mass. Each stage starts fresh with a better mass ratio, achieving more total delta-v.

    Ready to run the numbers?

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