Delta-v Calculator — Tsiolkovsky Rocket Equation
Calculate the total velocity change (Δv) a rocket can achieve — enter initial (wet) mass, final (dry) mass and specific impulse to apply the Tsiolkovsky rocket equation.
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Maximum velocity change in m/s — Tsiolkovsky rocket equation
- 1
Exhaust velocity ve = Isp × g₀
300 × 9.80665 = 2,942 - 2
Mass ratio m₀ ÷ mf
100,000 ÷ 20,000 = 5 - 3
Δv = ve × ln(mass ratio)
2,942 × ln(5) = 4,735Tsiolkovsky rocket equation — the logarithm reflects decreasing mass as fuel burns.
How does this calculator work?
Δv = Isp × 9.80665 × ln(m₀/mf). A rocket with Isp = 300 s and mass ratio 5 achieves Δv ≈ 4 734 m/s; mass ratio 10 gives ≈ 6 771 m/s. Reaching LEO requires ~9–10 km/s of Δv including gravity losses — typically achieved with multi-stage vehicles.
Formula
How this is calculated
The Tsiolkovsky rocket equation, derived in 1903, is the fundamental relation for propulsion in space. Because thrust comes from ejecting mass, the rocket gets lighter as fuel burns, so each kilogram of propellant produces more acceleration near the end of the burn than at the start — a logarithmic relationship. The equation is Δv = ve × ln(m₀/mf), where ve is effective exhaust velocity, m₀ is initial (fully fuelled) mass and mf is final (dry) mass after all propellant is consumed.
Exhaust velocity relates to specific impulse by ve = Isp × g₀ (g₀ = 9.80665 m/s²). Specific impulse, measured in seconds, is a propellant-agnostic efficiency measure independent of units: higher Isp means more Δv per kilogram of propellant. Chemical engines achieve roughly 250–460 s; nuclear thermal engines reach 800–1 000 s; ion thrusters reach 1 500–10 000 s. The trade-off is that high-Isp engines usually produce low thrust, making them impractical for launch but ideal for deep-space cruising.
Δv is the currency of spaceflight mission planning. Reaching low Earth orbit needs roughly 9–10 km/s (including gravity and drag losses not captured by this ideal equation). A Hohmann transfer from LEO to GEO adds ~3.9 km/s; trans-lunar injection from LEO adds ~3.2 km/s. Because propellant mass grows exponentially with Δv, high-Δv missions require staging or very high Isp propulsion.
Frequently asked questions
Approximately 9.0–9.5 km/s of ideal Δv, accounting for gravity drag and aerodynamic drag losses of roughly 1.5 km/s above the ~7.8 km/s orbital velocity. This calculator gives the ideal (vacuum, constant gravity) Δv from the rocket equation; real launches add a staging and trajectory penalty on top.
Practical chemical rockets achieve mass ratios of 5–20 (80–95% of launch mass is propellant). A ratio of 10 with Isp = 320 s gives Δv ≈ 7.2 km/s — not enough for a single stage to reach LEO from Earth, which is why multi-stage vehicles are used. Each stage is discarded when empty, effectively resetting the mass ratio.
No — the Tsiolkovsky equation gives ideal, loss-free Δv in a gravity-free vacuum. Real launches incur gravity drag (roughly 1–1.5 km/s for a vertical ascent) and atmospheric drag (roughly 0.1–0.3 km/s). For interplanetary cruising (already in orbit, far from planets) the ideal equation is an excellent approximation.
Also known as
TG we-Calculate Editorial Team. (2026). Delta-v Calculator — Tsiolkovsky Rocket Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/delta-v-calculator
TG we-Calculate Editorial Team. "Delta-v Calculator — Tsiolkovsky Rocket Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/delta-v-calculator.
TG we-Calculate Editorial Team, "Delta-v Calculator — Tsiolkovsky Rocket Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/delta-v-calculator
@misc{wecalculate_delta_v_calculator, title = {Delta-v Calculator — Tsiolkovsky Rocket Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/delta-v-calculator}}, year = {2026}, note = {TG we-Calculate} }
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