Mission Fuel Mass Calculator Formula

Understand the math behind the mission fuel mass calculator. Each variable explained with a worked example.

Use the Mission Fuel Mass Calculator

Formulas Used

Required Fuel Mass

fuel_mass = dry_mass * (exp(delta_v / exhaust_velocity) - 1)

Total Launch Mass

total_mass = dry_mass * exp(delta_v / exhaust_velocity)

Fuel Fraction

fuel_fraction = 1 - 1 / exp(delta_v / exhaust_velocity)

Variables

VariableDescriptionDefault
dry_massDry Mass (payload + structure)(kg)5000
delta_vRequired Delta-V(m/s)3000
exhaust_velocityExhaust Velocity(m/s)3000

How It Works

Mission Fuel Mass

From the Tsiolkovsky equation, the fuel needed for a given delta-v depends exponentially on the ratio dv/ve.

Formula

m_fuel = m_dry * (exp(dv / ve) - 1)

  • *m_dry* = payload plus structural mass
  • *dv* = required velocity change
  • *ve* = exhaust velocity

    • This shows why high delta-v missions are so demanding on fuel.

    Worked Example

    5000 kg dry mass, 3000 m/s delta-v, 3000 m/s exhaust velocity.

    dry_mass = 5000delta_v = 3000exhaust_velocity = 3000
    1. 01m_fuel = m_dry * (exp(dv/ve) - 1)
    2. 02dv/ve = 3000/3000 = 1
    3. 03exp(1) = 2.7183
    4. 04m_fuel = 5000 * (2.7183 - 1) = 5000 * 1.7183
    5. 05m_fuel = 8591 kg

    Frequently Asked Questions

    How does this change with multiple stages?

    Each stage is calculated independently. The payload of one stage becomes the total mass of the next, compounding the savings from discarding empty tanks.

    Why does fuel mass grow exponentially?

    The rocket must carry fuel to accelerate the remaining fuel. This feedback loop leads to exponential growth with delta-v.

    What is a typical fuel fraction for orbital launch?

    About 85% to 92% of the launch mass is propellant. Only 1-4% is payload for a single-stage system.

    Ready to run the numbers?

    Open Mission Fuel Mass Calculator