Tsiolkovsky rocket equation calculator

The rocket equation is brutal: delta-v grows only with the logarithm of the mass ratio, which is why rockets are almost entirely fuel.

Dry mass

Propellant mass

Specific impulse

Target delta-v

m/s

Delta-v available

7903.2m/s

≈ Rounded Rocket equation

Show the working

Dry mass = 5000
Propellant mass = 45 000
Specific impulse = 350
Target delta-v = 9400
Effective exhaust velocity = 350 * 9.80665 = 3432.33
wet_mass = 5000 + 45 000 = 50 000
Mass ratio = 5000 > 0 ? 50 000 / 5000 : 0 = 10
Delta-v available = 3432.33 * ln(10) = 7903.23
Mass ratio the target needs = exp(9400 / 3432.33) = 15.4663
Propellant for the target delta-v = 5000 * (15.4663 - 1) = 72 331.7
Propellant as a share of launch mass = 50 000 > 0 ? 45 000 / 50 000 * 100 : 0 = 90
Shortfall against the target = 9400 - 7903.23 = 1496.77

Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.

Scenarios & local history

The formula

delta-v = ve ln(m_wet / m_dry), with ve = Isp x g0
g0 is exactly 9.806 65 m/s2 by definition, which is why Isp in seconds works at all

Low Earth orbit needs about 9.4 km/s of delta-v including losses, which at 350 s Isp means a mass ratio near 15.6.

Specific impulse in seconds is exhaust velocity divided by standard gravity — a historical convention that survives because it is unit-agnostic.