Rocket Delta-V Calculator
Ideal rocket delta-v from specific impulse and mass ratio (Tsiolkovsky).
What it does
Rockets trade mass for speed, and Tsiolkovsky priced the trade in 1903. Burn propellant out the back and momentum pushes the rest forward; the faster the exhaust and the larger the mass fraction burned, the bigger the velocity change. One logarithm governs every chemical rocket ever flown.
The tool above runs the ideal equation: delta-v equals Isp times g0 times the log of launch over final mass. Enter impulse and both masses. It returns delta-v, the mass ratio, and the propellant share. Defaults of 350 s at ten to one open solved at 7,903 m/s with 90 percent fuel.
The logarithm is the tyranny everyone quotes. Doubling delta-v squares the mass ratio, so modest missions fly at 90 percent propellant while ambitious ones demand staging. Single stage to orbit fails on arithmetic before engineering starts.
Imperial and metric agree because physics does not read units. Ten to one at 350 s gives 7,903 m/s or 25,927 ft/s, the same speed in different rulers. Mass in pounds divides out of the ratio exactly as kilograms do.
Use the table for mission classes, then run the vehicle. Ideal means vacuum with no gravity: add 1 to 2 km/s of losses for real ascent, and stage when one ratio cannot afford the trip.
How to use
- Pick metric (kg, m/s) or imperial (lb, ft/s).
- Enter engine specific impulse in seconds.
- Enter full launch mass.
- Enter dry final mass.
- Read delta-v first, then ratio and share.
- Add gravity and drag for real missions.
Formula
- Isp
- Specific impulse in seconds.
- m0
- Full launch mass: kg metric, lb imperial.
- mf
- Burnout mass without propellant.
- g0
- 9.80665 m/s2 or 32.174 ft/s2.
Tsiolkovsky ideal rocket equation in vacuum with no external forces. g0 is 9.80665 metric or 32.174 ft/s2 imperial. Mass ratio above 1000 sits outside this teaching model. Real ascents add gravity and drag losses near 1 to 2 km/s.
Worked example
Example: Isp 350, mass ratio 10
Isp 350 s with 10000 kg launch and 1000 kg dry. Find ideal delta-v.
- Mass ratio: 10000 / 1000 = 10.
- Natural log: ln(10) = 2.3026.
- Exhaust velocity: 350 x 9.80665 = 3432.3 m/s.
- Delta-v: 3432.3 x 2.3026 = 7,903 m/s.
- Propellant share: (1 - 1/10) x 100 = 90%.
- NASA notes 90% propellant for orbit class missions.
Reference table
| Mass ratio | Delta-v | Reads as |
|---|---|---|
| 2 | 2,379 m/s | Half fuel, small maneuver |
| 5 (practice) | 4,735 m/s | 80% fuel, suborbital |
| 10 (worked) | 7,903 m/s | 90% fuel, orbit class |
Limits
- Ideal vacuum, no gravity or drag.
- Constant exhaust velocity assumed.
- Ratio above 1000 refused.
- Single burn; staging sums separately.
Common mistakes
- Forgetting gravity losses.
- Mixing weight with mass units.
- Using Isp in wrong seconds.
- Reading ideal as flight total.
- Skipping staging math.
Try it yourself
Quick checks. Answers sit tucked under each question.
Isp 300, 5000 kg to 1000 kg?
Ratio 5000 / 1000 = 5, ln 1.6094. 300 x 9.80665 x 1.6094 = 4,735 m/s with 80% fuel.
Imperial defaults in ft/s?
22046 / 2205 = 10, so 350 x 32.174 x 2.3024 = 25,927 ft/s, the same trip.
Mass ratio exactly 2 at Isp 350?
ln(2) = 0.693, so 350 x 9.80665 x 0.693 = 2,379 m/s with half the mass as fuel.
Questions
What is delta-v?
Maximum velocity change from expelling propellant with no outside forces. Maneuvers add linearly in delta-v budgets.
What is specific impulse?
Impulse per weight flow of propellant, in seconds. Chemical engines run 200 to 500, ion engines thousands.
Why does imperial match metric?
Multiply by 0.3048 in reverse: 7,903 m/s equals 25,929 ft/s. Both modes print the same physics.
How much reaches orbit?
About 9.4 km/s ideal for low orbit including losses; 7.5 flies only in a perfect vacuum with no gravity.
Why is staging needed?
Doubling delta-v squares the mass ratio. Ten to one gives one value; e to that power again needs a hundred to one.
Does ideal mean real?
No. Gravity and drag steal 1 to 2 km/s on ascent. The ideal number is the starting budget, never the flight total.