Work out rocket delta v instantly with clear inputs, formula shown and shareable results.
The Tsiolkovsky rocket equation gives delta-v as exhaust velocity times the natural log of the mass ratio. Burning 380 tonnes of a 500 tonne vehicle at 3000 m/s exhaust velocity yields 4283 m/s. The logarithm is the tyranny of the rocket equation: each additional increment of delta-v costs exponentially more propellant.
Tsiolkovsky equation
dv = ve x ln(m0 / mf)
Specific impulse
Isp = ve / g0
Because propellant must accelerate the propellant still aboard. Each kilogram of payload delta-v demands exponentially more fuel.
About 9.4 km/s from the ground including gravity and drag losses, against the 7.8 km/s of orbital velocity itself.