Formula Used
Δv = ve × ln(m0 ÷ mf)
ve = Isp × g0
m0 ÷ mf = eΔv ÷ ve
The natural logarithm links velocity capability with mass ratio. Higher exhaust velocity improves achievable delta-v. Real missions also include losses and reserves.
How to Use This Calculator
- Select the variable you need to calculate.
- Choose matching mass, velocity, and gravity units.
- Enter all known mass and propulsion values.
- Add losses, reserves, and performance reductions.
- Add stages when analyzing a staged vehicle.
- Submit the form and review both result groups.
- Export results with CSV, PDF, copy, or print.
Worked Example
A vehicle begins at 500,000 kilograms. It ends the burn at 120,000 kilograms. Its specific impulse is 450 seconds.
The effective exhaust velocity is about 4,413 meters per second. The mass ratio is about 4.167. Ideal delta-v is then about 6,297 meters per second.
Losses and reserves reduce usable mission performance. Always compare ideal and adjusted results carefully.
| Example | Initial mass | Final mass | Specific impulse | Approximate ideal delta-v |
|---|---|---|---|---|
| Small upper stage | 18,000 kg | 6,000 kg | 450 s | 4,848 m/s |
| Medium launcher stage | 120,000 kg | 30,000 kg | 350 s | 4,758 m/s |
| High-efficiency electric stage | 8,000 kg | 6,500 kg | 2,000 s | 4,070 m/s |
Assumptions and Limitations
The ideal equation assumes constant effective exhaust velocity. It ignores aerodynamic drag and gravity losses. It also treats burns as perfectly controlled.
Real vehicles experience throttling, steering, residual propellant, and structural effects. Mission planning needs trajectory simulation and verified engine data. This calculator supports early estimates only.
- No propellant slosh model is included.
- No engine throttling curve is simulated.
- No structural deformation model is included.
- No guidance or orbital mechanics solver is included.
- Preset mission values remain simplified references.
Calculation History
Recent summaries are stored in this browser.
Frequently Asked Questions
What does delta-v represent?
Delta-v measures a vehicle’s available velocity change. It is not ordinary travel speed. Mission maneuvers consume this capability.
Why must initial mass exceed final mass?
The vehicle loses propellant during the modeled burn. Therefore, burnout mass must remain smaller. Equal masses produce zero delta-v.
Can I enter specific impulse or exhaust velocity?
Yes. Enter either propulsion value when solving normally. The calculator converts between them using standard gravity.
What is mass ratio?
Mass ratio divides initial wet mass by final mass. Larger ratios can increase delta-v. Structural limits restrict practical values.
How are multi-stage results calculated?
Each stage uses its own mass ratio and propulsion value. Enter carried payload separately. Net stage values subtract entered losses.
Are mission presets exact?
No. They are simplified comparison values. Actual requirements depend on launch site, orbit, trajectory, and vehicle design.
Why is adjusted delta-v lower?
The adjusted value applies performance reductions and fixed losses. It also applies the selected safety margin. This creates a conservative estimate.
Can this calculator design a real rocket?
It supports preliminary engineering estimates only. Real design requires detailed simulation, testing, regulations, and qualified professional review.
What happens when payload capacity is negative?
The dry vehicle already exceeds allowable final mass. Reduce the target delta-v, improve propulsion, or reduce dry mass.