Free · Space mechanics
Ideal Rocket Delta-v from Exhaust Speed & Mass Ratio
Relate ideal velocity change to effective exhaust speed and initial/final mass using the Tsiolkovsky equation, with all four inverse paths.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
For mass ratio 2 and effective exhaust speed 1,000 m/s, ideal delta-v is 1,000 ln(2) m/s, approximately 0.693147 km/s.
Δv = vₑ ln(m₀ / m₁)
Worked example
Enter these known values and leave the other values blank.
- Effective exhaust speed vₑ
- 1000 m/s
- Initial total vehicle mass m₀
- 2 t
- Final total vehicle mass m₁
- 1 t
- Ideal velocity change Δv
- 0.6931 km/s
Assumptions and limitations
- Initial and final masses are positive, with initial mass greater than final mass. Both include the complete vehicle at their respective times.
- Effective exhaust speed is positive and constant. This model omits external forces, gravity losses and drag losses.
- The output is a velocity change, not absolute final speed, travel distance or time.
- The model is nonrelativistic. It does not account for staging or exhaust-speed changes during the mass loss.
Common questions
Why do mass units cancel?
The equation uses initial mass divided by final mass. Using the same mass unit for both leaves a dimensionless ratio.
Does doubling both masses change ideal delta-v?
No. If exhaust speed and the mass ratio stay the same, this ideal velocity change stays the same.
References
- NASA Glenn: ideal rocket equation
- NIST: SI and customary unit definitions
- Calculation definition and unit reference
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.