Calculate Δv, transfer time, and propellant mass for Hohmann transfer orbits between two circular orbits. Supports Earth, Mars, Moon, and custom central bodies.
The Hohmann transfer orbit is the most fuel-efficient two-impulse maneuver for moving a spacecraft between two coplanar circular orbits. Developed by Walter Hohmann in 1925, this elliptical transfer orbit touches the inner orbit at its periapsis and the outer orbit at its apoapsis, requiring exactly two engine burns.
This calculator computes both delta-v values (departure and arrival burns), the total Δv budget, the transfer time, and — using the Tsiolkovsky rocket equation — the propellant mass required for any given payload. It supports five preset central bodies (Earth, Mars, Moon, Sun, Jupiter) and allows custom gravitational parameters.
Whether you are a student solving orbital mechanics problems, an aerospace engineer planning mission trajectories, or a space enthusiast exploring mission scenarios, this calculator provides the fundamental parameters needed to evaluate a Hohmann transfer. The engine comparison table shows propellant requirements across chemical and electric propulsion systems. Check the example with realistic values before reporting.
Orbital mechanics involves large numbers, gravitational parameters, and the exponential nature of the rocket equation — all of which make mental arithmetic impossible. This calculator handles the vis-viva equation, transfer orbit geometry, and Tsiolkovsky mass ratio in one step, letting you compare mission scenarios rapidly and evaluate different propulsion technologies.
Hohmann Transfer: a_transfer = (r₁ + r₂) / 2 Δv₁ = |v_transfer,peri − v_circular,1| Δv₂ = |v_circular,2 − v_transfer,apo| Vis-viva equation: v = √(μ(2/r − 1/a)) Transfer time: t = π√(a³/μ) Tsiolkovsky rocket equation: Δv = Isp × g₀ × ln(m₀/m_f) m_propellant = m_payload × (e^(Δv/(Isp×g₀)) − 1)
Result: Δv ≈ 3935 m/s, transfer time ≈ 5.26 hours
A Hohmann transfer from LEO (6771 km radius) to GEO (42164 km radius) around Earth requires a total Δv of about 3935 m/s. The first burn (2457 m/s) enters the transfer ellipse, and the second burn (1478 m/s) circularizes at GEO. With Isp = 300 s, the mass ratio is 3.80, requiring 2800 kg of propellant for 1000 kg payload.
The vis-viva equation v = √(μ(2/r − 1/a)) is the key tool for computing velocities anywhere in an orbit. It relates the orbital speed at any distance r to the semi-major axis a and the gravitational parameter μ = GM. For circular orbits, r = a, giving v = √(μ/r). The Hohmann transfer calculation applies vis-viva at both the periapsis (inner orbit intersection) and apoapsis (outer orbit intersection) to find the transfer orbit velocities.
The Tsiolkovsky rocket equation Δv = Isp × g₀ × ln(m₀/m_f) shows that propellant mass grows exponentially with Δv. Doubling the Δv roughly squares the mass ratio. This exponential relationship is why high-Isp propulsion (ion engines, nuclear thermal) is so attractive for deep-space missions, even though these engines produce very low thrust and require longer transfer times.
While the Hohmann transfer is the foundation of orbital mechanics education, real mission designs often use more complex trajectories. Low-thrust spiral transfers use continuous electric propulsion. Gravity assists from planets provide essentially free Δv. Lagrange point orbits enable station-keeping with minimal fuel. Understanding the Hohmann transfer provides the baseline against which all these advanced techniques are compared.
It is an elliptical orbit that is tangent to both the initial and final circular orbits. The spacecraft fires its engine twice: once to enter the transfer ellipse and once to circularize at the target orbit. It is the most fuel-efficient two-burn maneuver between coplanar circular orbits.
Delta-v is the total change in velocity a spacecraft needs. It is the fundamental currency of orbital mechanics — every maneuver costs some Δv, and the total Δv budget determines how much propellant is needed via the Tsiolkovsky rocket equation.
Orbital mechanics equations use distance from the center of the gravitating body. For Earth, add 6371 km (mean radius) to the orbital altitude to get the orbit radius.
Isp measures engine efficiency — the thrust produced per unit of propellant consumed per second. Higher Isp means less propellant for the same Δv. Chemical rockets have Isp 250-450 s, while ion engines can reach 3000-5000 s.
The transfer time is half the orbital period of the transfer ellipse: t = π√(a³/μ). For LEO to GEO, this is about 5.3 hours. For Earth to Mars, it is about 259 days.
No. For very large orbit ratio changes (> ~12:1), a bi-elliptic transfer can use less total Δv. For time-critical missions, higher-energy transfers are faster. And gravity assists can provide "free" Δv by using planetary flybys.