Delta-v Calculator Formula

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

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Formulas Used

Delta-v

delta_v = exhaust_velocity * log(wet_mass / dry_mass)

Mass Ratio

mass_ratio = wet_mass / dry_mass

Variables

VariableDescriptionDefault
exhaust_velocityEffective Exhaust Velocity(m/s)3000
wet_massInitial (Wet) Mass(kg)100000
dry_massFinal (Dry) Mass(kg)10000

How It Works

The Tsiolkovsky Rocket Equation

dv = v_e * ln(m0 / mf)

  • *v_e* = effective exhaust velocity (or Isp × g0)
  • *m0* = initial mass with propellant
  • *mf* = final mass after burn
  • *ln* = natural logarithm

    • The mass ratio m0/mf determines how much velocity change is possible.

    Worked Example

    A stage: v_e = 3000 m/s, wet mass 100 000 kg, dry mass 10 000 kg.

    exhaust_velocity = 3000wet_mass = 100000dry_mass = 10000
    1. 01dv = v_e × ln(m0 / mf)
    2. 02Mass ratio = 100000 / 10000 = 10
    3. 03ln(10) ≈ 2.3026
    4. 04dv = 3000 × 2.3026 ≈ 6 908 m/s

    Frequently Asked Questions

    What is specific impulse?

    Specific impulse (Isp) measures engine efficiency in seconds. v_e = Isp × 9.80665 m/s².

    Why is the rocket equation exponential?

    The rocket must accelerate the remaining propellant too. Doubling dv requires squaring the mass ratio.

    How do multi-stage rockets help?

    Staging discards empty tanks so each stage does not accelerate dead weight, improving the effective mass ratio.

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