Delta-v budget
Delta-v calculator: Hohmann transfers and plane changes
Enter two altitudes, an inclination change, spacecraft mass and specific impulse (Isp). Get the delta-v (Δv) for each burn, the total, the coast time on a transfer, and the propellant mass that total costs. The next decision the number feeds is propulsion choice.
How this model works & what it omits
Two-body impulsive astrodynamics. Hohmann / plane-change / combined / circularize / deorbit, with a per-burn breakdown. Tsiolkovsky rocket equation for propellant mass. Keplerian trade-study accuracy - flight design needs finite-burn losses + numerical propagation.
This is a Hohmann transfer calculator and general impulsive-maneuver budgeter: it computes the burns for a Hohmann transfer, a pure plane change, a combined transfer-plus-plane-change, a circularization, and a deorbit burn from the vis-viva equation - two-body Keplerian astrodynamics with Earth's gravitational parameter μ = 398,600.4418 km³/s² (Space Mission Analysis and Design (SMAD) ch. 6–7; Vallado 2013, ch. 6) - then converts the total delta-v to propellant mass with the Tsiolkovsky rocket equation. It is an engineering trade-study tool: fast first-order numbers for sizing and comparison; flight design adds finite-burn losses and numerical propagation.
A spacecraft changes orbit by changing velocity. The size of that velocity change - the delta-v (Δv) - is the single number that sizes a propulsion system: it sets how much propellant you carry, which sets the wet mass, which sets the launch cost. Get the delta-v budget wrong early and the whole mass budget unravels. This tool budgets five canonical maneuvers, each a distinct two-body impulsive problem.
Hohmann transfer - the minimum-energy coplanar path between two circular orbits: a burn to enter an elliptical transfer orbit, a half-orbit coast, then a second burn to circularize at the target altitude. Plane change - a pure inclination rotation at fixed altitude, costing Δv = 2·v·sin(θ/2); it is brutally expensive at orbital speed, which is why launch directly into the right inclination whenever possible. Combined - a Hohmann transfer with the plane change folded into the second burn at apogee, where orbital speed is lowest and rotating the plane is cheapest; the apogee burn becomes the vector sum (law of cosines) of the circularization and rotation. Circularize - a single burn at apogee turning an elliptical orbit circular. Deorbit - a single retrograde burn lowering perigee into the atmosphere (typically 50-80 km) so atmospheric drag does the rest.
Orbital speeds come from the vis-viva equation v = √(μ·(2/r − 1/a)), with Earth's gravitational parameter μ = 398,600.4418 km³/s². Once the total delta-v is known, the Tsiolkovsky rocket equation m_p = m₀·(1 − e^(−Δv/v_e)) converts it to propellant mass, where the exhaust velocity v_e = I_sp·g₀ is set by the propulsion type - cold gas ~70 s, monopropellant ~220 s, bipropellant ~320 s, electric 1,000-3,000 s. Higher specific impulse means more delta-v per kilogram of propellant; the exponential makes high-Δv missions punishingly propellant-hungry on low-I_sp systems.
What this tool does not capture: finite-burn (gravity) losses from non-impulsive thrust, low-thrust spiral transfers (an electric-propulsion mission does not fly a Hohmann), J2 and third-body perturbations, plane-change savings from bi-elliptic transfers, launch-window and phasing constraints, and propulsion-system dry-mass scaling. It is an engineering trade-study tool - fast first-order numbers for sizing and comparison, not a flight-design propagator.
pick a maneuver, then dial orbit geometry and propulsion.
Maneuver
two-body impulsive astrodynamics.
Orbit geometry
only the fields the chosen maneuver uses are active.
Propulsion
Tsiolkovsky rocket equation: m_p = m0 (1 − e^(−Δv/ve)).
ve ≈ 2.157 km/s
Delta-v budget
Hohmann transfer (altitude change) · 2 burns
216.7 m/s
Total delta-v
19.11 kg
Propellant mass
9.6%
Propellant fraction
180.9 kg
Final (dry) mass
48.3 min
Transfer time
per-burn breakdown
50% of total budget
50% of total budget
delta-v by burn
Worked example
How much delta-v does a Hohmann transfer take?
This is the LEO altitude raise preset, and you can load it in the calculator above. A 200 kg spacecraft in a circular 400 km orbit raises to a circular 800 km orbit on a monopropellant system with a specific impulse (Isp) of 220 s. Two burns, one coast:
- 1. Perigee burn
- ~109 m/s
- enters the transfer ellipse
- 2. Coast
- ~48 min
- half the transfer orbit
- 3. Apogee burn
- ~108 m/s
- circularizes at 800 km
- Total Δv
- ~217 m/s
- costs ~19.1 kg of propellant
That is the intuition worth keeping for low Earth orbit (LEO): raising a circular orbit by a few hundred kilometres costs a couple of hundred metres per second. The 19.1 kg of propellant is 9.6% of the 200 kg wet mass, from the Tsiolkovsky rocket equation at 220 s Isp.
The next decision: what propulsion you fly
The delta-v is fixed by the orbits. The propellant is not: it is set by specific impulse through the rocket equation. At a delta-v this small the propellant tracks close to 1/Isp; the exponential only bites once the delta-v approaches the exhaust velocity. The same ~217 m/s on the same 200 kg wet mass:
| Propulsion | Isp | Propellant | Share of wet mass |
|---|---|---|---|
| Cold gas | ~70 s | ~54.1 kg | 27.1% |
| Monopropellant | ~220 s | ~19.1 kg | 9.6% |
| Bipropellant | ~320 s | ~13.3 kg | 6.7% |
Cold gas costs about four times the propellant of bipropellant for the identical maneuver, a difference of roughly 40 kg in propellant allocation. That is not a like-for-like system comparison: this model excludes propulsion hardware dry-mass scaling, so the tank, feed system and thrusters still have to be sized before you know what the change is worth. Electric propulsion is deliberately absent from the table: a low-thrust vehicle spirals rather than flying a two-impulse Hohmann, so this page's impulsive model does not cover the trajectory it would fly. Once you have picked a row, the CubeSat propulsion calculator sizes the tank, thruster and burn time around it.
