Tsiolkovsky Rocket Equation Calculator
Delta-v from wet mass, dry mass and specific impulse — or the propellant needed for a target Δv — with mass ratio, propellant fraction, exhaust velocity and burn time at a given thrust.
How it works
Δv = v_e · ln(m₀ ÷ m_f), v_e = Isp × 9.80665; m₀ = m_f · e^(Δv/v_e); burn time = propellant ÷ (thrust ÷ v_e)
The rocket equation is the tyranny of spaceflight: because propellant must lift the propellant burned later, the required mass ratio grows exponentially with Δv. Reaching low Earth orbit needs about 9.4 km/s including losses; with kerosene engines (v_e ≈ 3 km/s) that is a mass ratio of 22 — impossible for one stage, which is why rockets stage. Higher Isp helps exponentially, which is the appeal of hydrogen and, for deep space, ion engines.
Worked example
Falcon 9 first stage: 549 t wet, 138 t after burnout (with upper stage), Isp 311 s → Δv = 3,050 × ln(3.98) = 4,210 m/s; at 7,607 kN the 411 t of propellant burns for 165 s.
Frequently asked questions
Why does staging help?
Dropping empty tanks lowers m_f for the next burn, so each stage’s Δv adds without carrying dead mass all the way.
What about gravity and drag losses?
They add roughly 1.5 km/s to the ideal 7.8 km/s orbital speed; the equation gives the ideal Δv the vehicle can produce.
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This calculator is for educational purposes. Double-check important results before acting on them.