Tsiolkovsky Rocket Equation Calculator
This calculator uses the Tsiolkovsky rocket equation for the ideal case where thrust is applied in a constant direction and no other forces (gravity, atmospheric drag, etc.) act on the rocket.
Equation: Δv = veff × ln(m0 / mf)
Alternatively (using specific impulse): Δv = Isp × g₀ × ln(m0 / mf) where g₀ = 9.80665 m/s²
Example: A single-stage rocket has a specific impulse of 300 seconds. The initial total mass with propellant is 1000 kg, and the final dry mass without propellant is 100 kg. Calculate the change in velocity Δv and the effective exhaust velocity veff (neglecting gravity and drag).
To calculate, enter any three values (use either veff or Isp for the exhaust parameter, or both if they are consistent). The fourth value will be calculated automatically. The alternative exhaust field (veff or Isp) will also be filled if left blank.
Δv for Other Solar System Transfers
| Transfer | Approximate Δv (km/s) | Notes |
|---|---|---|
| LEO → Venus low orbit | ~3.5 – 4.0 | Hohmann-like transfer + capture; aerocapture common |
| LEO → Mercury low orbit | ~7.0 – 8.0 | Deep solar well; gravity assists usually required |
| LEO → Jupiter low orbit | ~6.3 – 7.0 | Gravity assists strongly reduce real-mission Δv |
| LEO → Saturn low orbit | ~7.0 – 8.0 | Gravity assists required in practice |
| LEO → Sun impact/graze | ~25 – 30 | Near-total cancellation of Earth's ~30 km/s orbital velocity |
| Lunar surface → Mars low orbit | ~6.0 – 6.5 | Ascent + interplanetary transfer; aerobraking at Mars (higher than from LEO due to reduced Oberth benefit) |
Notes: Values are approximate idealized propulsive Δv for efficient trajectories (e.g., Hohmann or bi-elliptic). Real missions frequently use gravity assists, aerobraking/aerocapture, and optimal launch windows to reduce requirements substantially. Lunar values assume surface start; Mars values assume low orbit start (aerobraking used where noted). Does not include launch from Earth's surface to LEO (~9.4 km/s with losses).
Sources: Standard delta-v maps (Wikipedia, Atomic Rockets, mission analyses).
Δv Reduced with Maximum Gravity Assists
| Transfer | Approximate Reduced Δv (km/s) | Notes |
|---|---|---|
| LEO → Venus low orbit | ~3.5 – 4.0 | Direct optimal; gravity assists provide little further reduction |
| LEO → Mercury low orbit | ~4.0 – 5.0 | Significant reduction vs direct (~7–8 km/s); multiple Venus/Earth/Mercury assists (MESSENGER-like) |
| LEO → Mars low orbit | ~4.0 – 4.5 | Aerobraking common; gravity assists offer limited reduction |
| LEO → Jupiter low orbit | ~4.5 – 5.5 | Major reduction vs direct; VEEGA + propulsive capture (Galileo-like) |
| LEO → Saturn low orbit | ~5.0 – 6.0 | Major reduction vs direct; VVEJGA + propulsive capture (Cassini-like) |
| LEO → Sun (close approach/graze) | ~3.5 – 8.0 | Significant potential reduction with multiple Venus assists (concepts); Parker Solar Probe used high-energy launch (~12 km/s v∞ equivalent) for faster timeline |
| Low Mars orbit → LEO | ~2.9 – 3.5 | Direct trans-Earth injection + aerobraking; gravity assists (e.g., Venus) offer minor reduction |
| Low Mars orbit → Venus low orbit | ~3.0 – 4.5 | Direct or with assists; generally comparable to Earth-origin |
| Low Mars orbit → Jupiter low orbit | ~4.5 – 6.0 | Approximate; possible Earth/Venus assists for reduction |
| Low Mars orbit → Sun (close approach) | ~10 – 20 | Lower orbital velocity than Earth helps; multiple Venus assists can reduce further |
| Phobos surface → LEO | ~2.5 – 3.0 | Low gravity advantage (negligible takeoff/landing Δv); ~2.88 km/s from older delta-v charts for Earth return + aerobraking |
| Phobos surface → Venus low orbit | ~3.0 – 4.0 | Similar advantage over Mars surface departure; approximate based on positioning |
| Phobos surface → Jupiter low orbit | ~4.0 – 5.5 | Low-gravity staging benefit; gravity assists possible |
| Phobos surface → Sun (close approach) | ~8 – 15 | Benefit from Mars distance + low escape; assists can reduce |
Notes: Values are approximate propulsive Δv using extensive gravity assists for maximum reduction (often longer mission durations). Real missions (e.g., Galileo, Cassini, MESSENGER, Parker) demonstrate significant savings for challenging destinations, primarily via lower launch energy (C3) and trajectory shaping. Aerobraking/aerocapture assumed where applicable. Phobos values benefit from extremely low surface escape (~0.01 km/s) and higher starting orbit around Mars. Direct transfers (previous table) are often faster but more Δv-intensive. Sources include mission data, delta-v budgets, and astrodynamics references.