Rocket equation
Δv = g₀ I_sp ln(m₀/m_f)
Ideal velocity capability from mass ratio and specific impulse.
Rocket Equation Delta-V Calculator
Estimate ideal Tsiolkovsky delta-v from initial mass, final mass, and specific impulse, with an optional lumped loss allowance.
Access: Free to use, no installation, and No account required.
Inputs
This is an ideal single-stage mass-ratio model. Gravity loss, drag, steering, finite burns, changing Isp, staging, residuals, margins, and structural constraints require a fuller trajectory/vehicle model.
Results
Tsiolkovsky rocket equation
Ideal delta-v is Δv = g₀Isp ln(m₀/mf). Because mass ratio is inside a logarithm, increasingly large propellant fractions provide diminishing delta-v returns.
Engineering reference
Rocket Equation Delta-V Calculator: background and worked detail
Use the Rocket Equation Delta-V Calculator to estimate ideal Tsiolkovsky delta-v, net delta-v after an entered loss allowance, mass ratio, propellant mass, and propellant fraction from initial mass, final mass, and specific impulse.
Why mass ratio dominates delta-v
The Tsiolkovsky equation integrates thrust from propellant mass loss under an idealized constant effective exhaust velocity. Specific impulse converts to effective exhaust velocity through standard gravity.
The equation is foundational for mission mass budgeting but does not determine whether a vehicle can produce enough thrust, survive atmospheric flight, meet structural margins, or execute finite burns and staging efficiently.
Equations used by this calculator
Mass ratio
MR = m₀/m_f
Initial mass divided by final mass after the modeled propellant is expended.
Propellant fraction
f_p = (m₀−m_f)/m₀
Fraction of initial mass consumed as propellant in the modeled burn.
10,000 kg initial, 4,000 kg final, 320 s Isp
Use m0 = 10,000 kg, mf = 4,000 kg, Isp = 320 s, and zero entered losses.
- Mass ratio is 2.5.
- Propellant mass is 6,000 kg, or 60% of initial mass.
- Ideal delta-v is about 2.88 km/s.
Result: Any gravity, drag, steering, reserve, or performance loss entered by the user is subtracted from the ideal result as a simple allowance.
Ideal delta-v excludes real losses
Assumptions
- Specific impulse is constant over the modeled burn.
- The system is treated as a single ideal rocket stage for the equation.
- Losses, if entered, are represented by a single scalar delta-v subtraction.
Limitations
- Does not model staging, thrust-to-weight ratio, finite burns, atmospheric drag, gravity losses, steering losses, throttle variation, mixture ratio, tankage, or reserve policy in detail.
- High mission fidelity requires trajectory and propulsion simulation.
Validation checks
No propellant used
Case: Set initial mass equal to final mass.
Expected: Ideal delta-v should be zero.
Mass-ratio effect
Case: Increase m0/mf with Isp fixed.
Expected: Ideal delta-v should increase logarithmically, not linearly.
Rocket Equation Delta-V Calculator FAQ
Why does adding propellant have diminishing returns?
Delta-v depends on the natural logarithm of mass ratio, so each additional increase in mass ratio produces a smaller incremental delta-v.
What is specific impulse?
Specific impulse is a propulsion efficiency metric in seconds; multiplying by standard gravity gives effective exhaust velocity.
Should gravity and drag losses be subtracted from rocket-equation delta-v?
For a rough mission budget, yes, but real losses depend on trajectory, thrust, atmosphere, steering, and burn timing and should be simulated when accuracy matters.
Where this calculation comes from
Shared with the Rocket Propulsion Workbench, which adds staging, gravity losses, and engine performance modelling.
Open the source workbench →Read calculation and source methodology →