Rocket Equation Calculator
The Rocket Equation Calculator solves the Tsiolkovsky equation (ΔV = Isp × g₀ × ln(m₀/mf)) for any unknown variable. It supports multi-stage rocket analysis with per-stage ΔV breakdown, includes engine presets (Merlin, Raptor, RS-25), and displays an interactive SVG stage separation diagram — free, no signup required.
Single-Stage Calculator
Multi-Stage Rocket
ΔV Budget Reference
| Mission Target | Required ΔV (m/s) |
|---|---|
| Low Earth Orbit (LEO) | 9,400 |
| Geosynchronous Transfer | 12,000 |
| Lunar Orbit | 15,900 |
| Lunar Surface | 18,200 |
| Mars Transfer | 15,700 |
| Mars Orbit | 17,900 |
| Jupiter Transfer | 24,000 |
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What is the Tsiolkovsky Rocket Equation?
The Tsiolkovsky rocket equation (ΔV = Isp × g₀ × ln(m₀/mf)) is the fundamental equation of astronautics that describes the relationship between a rocket's change in velocity (delta-V), its specific impulse (Isp), and its mass ratio. Derived by Konstantin Tsiolkovsky in 1903, it shows that a rocket's delta-V depends logarithmically on the ratio of its initial mass (including propellant) to its final mass (after propellant is expended). This equation is used to design every space mission, from satellite launches to interplanetary transfers, and demonstrates why multi-stage rockets are essential for reaching orbit.
How to Use This Calculator
- Select what you want to solve for: ΔV, payload mass, propellant mass, or specific impulse
- Enter the known values or select an engine preset (Merlin, Raptor, RS-25, etc.)
- Click Calculate to see the result with mass ratio and propellant fraction
- Use the Multi-Stage tab to analyze rockets with up to 5 separate stages
- Check the ΔV Budget table to see if your rocket can reach its target orbit
Frequently Asked Questions
What is delta-V and why is it important?
Delta-V (ΔV) is the total change in velocity a rocket can achieve. It's the universal currency of space travel — every maneuver (launch, orbit change, landing) costs a specific amount of ΔV. For example, reaching low Earth orbit requires about 9,400 m/s of ΔV. The rocket equation tells you how much propellant you need to achieve a given ΔV.
Why are multi-stage rockets more efficient?
Multi-stage rockets discard empty fuel tanks as they ascend, reducing the mass that remaining engines must accelerate. The rocket equation shows that ΔV depends on ln(m₀/mf) — by staging, each subsequent stage has a much better mass ratio. A single-stage rocket carrying all structure to orbit wastes ΔV pushing empty tanks, while staging can increase total ΔV by 30-50%.
What is specific impulse (Isp)?
Specific impulse (Isp) measures how efficiently a rocket engine uses propellant, expressed in seconds. It represents the thrust produced per unit weight of propellant consumed per second. Higher Isp means more ΔV per kilogram of propellant. Chemical rockets range from 200-460s, while ion engines can achieve 1,000-10,000s but with much lower thrust.