Hohmann Transfer Orbit Calculator
Compute the two-burn delta-v budget and transfer time for a Hohmann orbit transfer between any two circular orbits, from LEO-to-GEO to Earth-to-Mars interplanetary missions.
🌍 What is the Hohmann Transfer Orbit Calculator?
A Hohmann transfer orbit is the most fuel-efficient two-impulse maneuver to move a spacecraft from one circular orbit to another circular coplanar orbit around the same gravitational body. Proposed by German engineer Walter Hohmann in 1925, the transfer uses an intermediate ellipse whose periapsis (closest point) lies on the initial orbit and whose apoapsis (farthest point) lies on the target orbit. Two propulsive burns execute the transfer: the first burn raises or lowers the orbit to intersect the target, and the second burn circularizes at the target altitude.
This calculator has two modes. Orbit Around a Body covers transfers around Earth (LEO to GEO, parking orbit to lunar distance, etc.), Moon, Mars, Venus, and Jupiter. You enter the initial and target orbit altitudes above the body's surface, and the calculator returns both individual burns (delta-v1 and delta-v2), the total delta-v budget, the transfer time, and the spacecraft velocity in the transfer orbit at each endpoint. This covers the most common use cases in spacecraft trajectory design: orbit raising and lowering maneuvers, station-keeping adjustments, and satellite deployment sequences.
Interplanetary mode covers heliocentric Hohmann transfers between planetary orbits. Select any two planets from Mercury through Neptune, or enter custom orbital radii in astronomical units (AU). The calculator shows the delta-v required at departure (to move from the planetary orbit onto the transfer ellipse) and at arrival (to circularize at the target), along with the transfer time in days and years. Note that interplanetary results are heliocentric values only and do not include the planetary departure or capture burns within each planet's gravity well, which add several km/s to real mission budgets.
Both modes use exact Keplerian two-body mechanics with precise gravitational parameters (mu) for the central body. The results agree to within 0.5% of published NASA mission planning values for standard transfers.
📐 Formulas
Δv⊂1; = |√ (μ × (2/r⊂1; − 1/a)) − √ (μ/r⊂1;)|
Δv⊂1; = delta-v for first burn at r⊂1; (m/s)
μ = gravitational parameter of central body (m³/s²)
r⊂1; = initial orbit radius from body center (m)
a = (r⊂1; + r⊂2;) / 2 = semi-major axis of transfer ellipse (m)
Δv⊂2; = |√ (μ/r⊂2;) − √ (μ × (2/r⊂2; − 1/a))|
Δv⊂2; = delta-v for second burn at r⊂2; (m/s)
r⊂2; = target orbit radius from body center (m)
Example: r⊂1; = 6778 km (LEO 400 km), r⊂2; = 42164 km (GEO): a = 24471 km, Δv⊂1; = 2.40 km/s, Δv⊂2; = 1.46 km/s
t⊂transfer; = π × √ (a³ / μ)
t⊂transfer; = one-way transfer time (seconds) = half the orbital period of the transfer ellipse
Example: LEO to GEO: t = π × √ ((24471000)³ / 3.986×10¹&sup4;) = 19,050 s = 5.29 hours
📖 How to Use This Calculator
Steps
1
Select a central body and enter orbit altitudes - In Orbit Around a Body mode, choose a central body from the dropdown (Earth, Moon, Mars, Venus, or Jupiter) and enter the initial orbit altitude h1 and target orbit altitude h2 in kilometres above the surface.
2
Read the delta-v budget and transfer time - The results show total delta-v (km/s), first burn dv1, second burn dv2, transfer time, and the spacecraft's velocity in the transfer orbit at both endpoints. These are the minimum theoretical values for a two-burn transfer.
3
Switch to Interplanetary mode for solar system missions - Click the Interplanetary tab. Select source and target planet presets or enter custom orbit radii in AU. The AU values fill automatically from the planet select; you can override them for custom trajectories.
4
Use the target orbit slider to explore the delta-v curve - In Interplanetary mode, drag the target orbit radius slider from 0.3 to 32 AU to see how delta-v and transfer time change across the solar system in real time. Watch the transfer time grow dramatically for outer planets.
5
Chain with Tsiolkovsky to get propellant mass - Take the total delta-v output and enter it into the Tsiolkovsky Rocket Equation Calculator with your engine Isp to find the required propellant mass fraction for your mission.
💡 Example Calculations
Example 1 - LEO to GEO Transfer (Geostationary Orbit Insertion)
Earth orbit: h⊂1; = 400 km (ISS-like LEO) to h⊂2; = 35786 km (GEO)
1
Compute orbital radii: r1 = 6378.1 + 400 = 6778.1 km = 6,778,100 m. r2 = 6378.1 + 35786 = 42,164.1 km = 42,164,100 m. Semi-major axis: a = (6778100 + 42164100) / 2 = 24,471,100 m.
2
Circular orbit speeds: v1_circ = sqrt(3.986e14 / 6778100) = 7669 m/s. v2_circ = sqrt(3.986e14 / 42164100) = 3074 m/s. Transfer orbit perigee: vT1 = sqrt(3.986e14 x (2/6778100 - 1/24471100)) = 10,066 m/s. Transfer orbit apogee: vT2 = sqrt(3.986e14 x (2/42164100 - 1/24471100)) = 1618 m/s.
3
Burns: dv1 = 10066 - 7669 = 2397 m/s. dv2 = 3074 - 1618 = 1456 m/s. Total dv = 3853 m/s = 3.853 km/s. Transfer time = pi x sqrt(24471100^3 / 3.986e14) = 19,050 s = 5.29 hours.
Δv = 3.853 km/s, transfer time = 5.29 hours
Try this example →Example 2 - Earth to Mars Interplanetary Hohmann
Heliocentric transfer from Earth (1.000 AU) to Mars (1.524 AU)
1
Orbit radii: r1 = 1.000 x 1.496e11 = 1.496e11 m. r2 = 1.524 x 1.496e11 = 2.280e11 m. Semi-major axis: a = 1.888e11 m = 1.262 AU.
2
Earth orbital velocity: v1_circ = sqrt(1.327e20 / 1.496e11) = 29,784 m/s. Transfer orbit at r1: vT1 = sqrt(1.327e20 x (2/1.496e11 - 1/1.888e11)) = 32,729 m/s. dv1 = 32729 - 29784 = 2945 m/s.
3
Mars orbital velocity: v2_circ = sqrt(1.327e20 / 2.280e11) = 24,134 m/s. Transfer orbit at r2: vT2 = sqrt(1.327e20 x (2/2.280e11 - 1/1.888e11)) = 21,492 m/s. dv2 = 24134 - 21492 = 2642 m/s. Total dv = 5587 m/s. Transfer time = pi x sqrt((1.888e11)^3 / 1.327e20) = 22,394,000 s = 259 days.
Δv = 5.587 km/s (heliocentric), transfer time = 258.9 days
Try this example →Example 3 - LEO to Lunar Transfer Orbit (Earth-Moon)
Earth orbit: h⊂1; = 400 km (LEO) to approximate lunar distance 384,000 km altitude
1
r1 = 6778.1 km, r2 = 6378.1 + 384000 = 390378.1 km. a = (6778.1 + 390378.1) / 2 = 198578.1 km = 198,578,100 m. v1_circ = sqrt(3.986e14 / 6778100) = 7669 m/s.
2
Transfer perigee: vT1 = sqrt(3.986e14 x (2/6778100 - 1/198578100)) = sqrt(3.986e14 x 2.904e-7) = sqrt(115,815,000) = 10,762 m/s. dv1 = 10762 - 7669 = 3093 m/s.
3
v2_circ at lunar distance = sqrt(3.986e14 / 390378100) = sqrt(1021000) = 1010 m/s. Transfer apogee: vT2 = sqrt(3.986e14 x (2/390378100 - 1/198578100)) = sqrt(3.986e14 x 9.77e-9) = sqrt(3893000) = 1973 m/s. dv2 = 1973 - 1010 = 963 m/s. Total = 4056 m/s. Transfer time = pi x sqrt((1.986e8)^3 / 3.986e14) = 432,000 s = 5.0 days.
Δv = 4.056 km/s, transfer time = 5.0 days
Try this example →Example 4 - Earth to Jupiter Interplanetary Transfer
Heliocentric transfer from Earth (1.000 AU) to Jupiter (5.203 AU)
1
r1 = 1.496e11 m, r2 = 5.203 x 1.496e11 = 7.784e11 m. a = (1.496e11 + 7.784e11) / 2 = 4.640e11 m = 3.101 AU.
2
Earth v1_circ = 29,784 m/s. Transfer at r1: vT1 = sqrt(1.327e20 x (2/1.496e11 - 1/4.640e11)) = sqrt(1.327e20 x 1.119e-11) = sqrt(1.485e9) = 38,533 m/s. dv1 = 38533 - 29784 = 8749 m/s.
3
Jupiter v2_circ = sqrt(1.327e20 / 7.784e11) = 13,064 m/s. Transfer at r2: vT2 = sqrt(1.327e20 x (2/7.784e11 - 1/4.640e11)) = sqrt(1.327e20 x 4.16e-12) = sqrt(5.52e8) = 7420 m/s. dv2 = 13064 - 7420 = 5644 m/s. Total = 14,393 m/s. Transfer time = 2.732 years.
Δv = 14.393 km/s (heliocentric), transfer time = 2.73 years
Try this example →❓ Frequently Asked Questions
What is a Hohmann transfer orbit and how does it work?
A Hohmann transfer orbit is an ellipse tangent to both the initial and target circular orbits. The spacecraft fires its engine at the initial orbit tangentially (prograde) to enter the ellipse, coasts for half an orbital period, then fires again tangentially at the target orbit to circularize. Because both burns are tangential (parallel to the current velocity), no energy is wasted changing direction, making this the most fuel-efficient two-burn transfer between coplanar circular orbits. The concept was mathematically proven by Walter Hohmann in his 1925 paper Die Erreichbarkeit der Himmelskorper (The Attainability of Celestial Bodies).
How much delta-v does a LEO to GEO transfer require?
From a 400 km circular LEO to GEO at 35786 km: dv1 = 2.40 km/s, dv2 = 1.46 km/s, total = 3.85 km/s. From a 185 km circular orbit: dv1 = 2.44 km/s, dv2 = 1.47 km/s, total = 4.21 km/s. Real GEO insertion missions typically budget about 4.2 to 4.5 km/s total when accounting for gravity losses during finite burns, inclination changes, and trajectory corrections, compared to the theoretical 3.9 to 4.2 km/s from the two-body Hohmann calculation.
Why is the Hohmann transfer the minimum delta-v path?
The Hohmann transfer minimizes delta-v because both burns are applied tangentially at the exact apses of the transfer ellipse, where the velocity vectors of the circular orbit and the transfer ellipse are parallel. Any other two-burn transfer would require either burns that are not tangential (wasting propellant on direction changes) or an ellipse that does not intersect both target orbits tangentially. The Hohmann transfer satisfies the necessary conditions for minimum-energy two-impulse transfer as proven in optimal control theory.
What is the Earth to Mars Hohmann transfer time and delta-v?
The heliocentric Hohmann from Earth (1.000 AU) to Mars (1.524 AU) requires dv1 = 2.94 km/s (departure from Earth orbit onto the transfer ellipse), dv2 = 2.64 km/s (arrival at Mars orbit), total heliocentric delta-v = 5.58 km/s, and a transfer time of 258.9 days. The actual mission delta-v from low Earth orbit adds about 3.6 km/s to escape Earth plus about 1.0 km/s to capture at Mars, making the total from LEO approximately 9.5 to 10.0 km/s for a fully propulsive Mars mission.
When is a bi-elliptic transfer more efficient than Hohmann?
A bi-elliptic transfer (three burns: first raises apoapsis to a very high intermediate orbit, second circularizes partially, third completes the transfer) is more efficient than a Hohmann transfer when the orbit ratio r2/r1 exceeds about 11.94. This is because at very high orbit ratios, the large first burn in a bi-elliptic transfer, applied at the most favourable (low-speed, high-energy) point in the intermediate orbit, can out-compete the large second Hohmann burn applied at a slower point. For most practical Earth missions (r2/r1 up to 6.2 for LEO to GEO), Hohmann is optimal.
Does the Hohmann transfer work for non-circular initial orbits?
The classic Hohmann transfer assumes both initial and final orbits are circular and coplanar. For elliptical initial orbits, the equivalent procedure is either a Hohmann from the apoapsis or periapsis (taking the circular orbit velocity at that radius as the reference) or a more general Lambert's problem solution. For inclined orbits, combined plane-change and altitude-change maneuvers are used, and the optimal burn split between the two burns and the plane change depends on the specific geometry. This calculator computes only the classical circular-to-circular coplanar case.
How do I find the propellant mass needed for a Hohmann transfer?
Use the Tsiolkovsky rocket equation for each burn: m_prop = m_final x (e^(dv/(Isp x g0)) - 1). For a spacecraft with dry mass 1000 kg and an engine with Isp = 320 s performing a LEO-to-GEO transfer (total dv = 3.85 km/s), each stage requires separate calculation because the mass changes after each burn. For the two burns combined, total propellant mass = 1000 x (e^(3850/3137) - 1) = 1000 x (e^1.228 - 1) = 1000 x 2.414 = 1414 kg, giving a total initial mass of 2414 kg. Use the Tsiolkovsky Rocket Equation Calculator on this site for the exact per-stage breakdown.
What is the gravitational parameter mu used in the formulas?
The gravitational parameter mu = G x M_body, where G = 6.674e-11 m^3/(kg x s^2) and M is the body mass. Using mu directly avoids multiplying two large numbers. Values used in this calculator: Earth mu = 3.986004418e14 m^3/s^2, Moon mu = 4.9048695e12 m^3/s^2, Mars mu = 4.282837e13 m^3/s^2, Venus mu = 3.24858592e14 m^3/s^2, Jupiter mu = 1.26686534e17 m^3/s^2, Sun mu = 1.32712440018e20 m^3/s^2. These values are from the IAU 2012 recommendations and JPL DE430 planetary ephemeris.
How does the transfer time depend on the orbit radii?
Transfer time t = pi x sqrt(a^3/mu) where a = (r1+r2)/2. For fixed r1, t scales with r2 approximately as r2^(3/2) for r2 much greater than r1. Representative Earth-based transfer times: LEO to GEO (400 to 35786 km): 5.3 hours; LEO to lunar distance (400 to 384000 km): 5.0 days; LEO to Sun-Earth L1 (1.5e6 km): 3.5 months. Representative interplanetary: Earth to Venus: 146 days; Earth to Mars: 259 days; Earth to Jupiter: 2.73 years; Earth to Saturn: 6.05 years; Earth to Neptune: 30.7 years.
What is the Tsiolkovsky equation and how do I use Hohmann delta-v with it?
The Tsiolkovsky rocket equation is delta-v = Isp x g0 x ln(m0/mf), where Isp is specific impulse in seconds, g0 = 9.807 m/s^2, m0 is initial wet mass, and mf is final dry mass. Rearranging: m0/mf = e^(delta-v / (Isp x g0)). For a LEO-to-GEO mission with total delta-v = 3.85 km/s and an upper stage with Isp = 450 s (LOX/LH2): mass ratio = e^(3850/(450 x 9.807)) = e^0.872 = 2.39. So 58% of the initial mass is propellant. Enter the Hohmann total delta-v into the Tsiolkovsky Calculator to get the exact propellant fraction for your mission's Isp.
Can I use the Hohmann calculator for lunar orbit transfers?
Yes, but with an important caveat. The Orbit Around a Body mode using Earth and entering the lunar distance as a target altitude (384000 km) gives a Keplerian estimate of the delta-v to reach lunar distance from LEO. However, once the spacecraft enters the Moon's sphere of influence (about 66000 km from the Moon), the Moon's gravity dominates and the two-body Earth-centred calculation is no longer valid. Actual lunar transfer trajectories use patched-conic methods or full n-body integration. The Hohmann estimate of about 3.9 to 4.1 km/s from LEO to translunar injection is approximately correct but should be verified with more detailed trajectory design tools for mission planning.
What is the phase angle required for a Hohmann transfer departure?
The target body must be at a specific lead angle ahead of the spacecraft at departure so it arrives at the transfer orbit apoapsis at the same time as the target. Phase angle at departure = pi - n2 x t_transfer, where n2 = sqrt(mu/r2^3) is the target's mean motion and t_transfer is the Hohmann transfer time. For Earth to Mars: n_Mars = 9.07e-7 rad/s, t = 2.239e7 s, phase angle = pi - 9.07e-7 x 2.239e7 = pi - 20.31 rad = pi - (20.31 mod 2pi) rad = pi - 1.76 rad = 1.38 rad = 79 degrees. Mars must be 79 degrees ahead of Earth at departure for a direct Hohmann transfer arrival.