Rocket Equation & Staging Δv Calculator

Applies the Tsiolkovsky rocket equation, Δv = Isp · g0 · ln(m0 / mf), to a stack of up to four stages sitting on a payload. Each stage is described by its propellant mass, its dry mass (tanks, engines and structure left after the burn) and its specific impulse; the tool works out the mass at ignition of every stage — everything still above it included — and gives each stage's Δv, the total, the lift-off mass and the ratio of lift-off mass to payload. Add a stage's thrust and it also gives the burn time and the thrust-to-weight ratio at ignition and at burnout, and warns when the first stage cannot lift itself off the pad. The second mode runs the equation backwards: for a target Δv, a dry mass and an Isp it returns the propellant needed and the propellant fraction, which shows how fast the exponential bites — 9.4 km/s at 450 s already needs about 7.4 kg of propellant for every kilogram of dry mass. The Δv values are checked by numerically integrating thrust and mass flow rather than trusting the logarithm. What the equation does not include: gravity losses during a slow ascent, aerodynamic drag, steering losses, and the fall of Isp at sea level compared with vacuum — together these typically add 1.5 to 2 km/s to what a launch to low Earth orbit really needs, so compare the total here with about 9.4 km/s, not with the 7.8 km/s orbital speed. Staging events are treated as instantaneous and interstages or fairings as part of a stage's dry mass.