How this calculator works
Tsiolkovsky's equation balances momentum as a rocket expels propellant. Because the vehicle becomes lighter during the burn, velocity change depends logarithmically on the ratio of initial to final mass. Use an effective exhaust velocity that already includes any pressure-thrust contribution. This is one ideal stage, with no atmospheric drag or external gravitational impulse.
Formula
delta-v = ve ln(m0/mf). ve = delta-v/ln(m0/mf). Mass ratio = exp(delta-v/ve). Propellant fraction = 1-mf/m0.
Worked example
A 2 kg rocket ending at 1 kg with ve = 1000 m/s gains 693.147 m/s ideally. A 4 kg rocket making that same velocity change ends at 2 kg.
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Frequently asked questions
Why is the logarithm natural?
Integrating the momentum balance over changing vehicle mass gives the natural logarithm.
Does a larger rocket get more delta-v?
Scaling both masses equally leaves their ratio, and therefore ideal delta-v, unchanged.
Can I use this for several stages?
Calculate each stage separately with the mass it actually carries, then add the ideal velocity increments.