Hohmann Transfer — Time of Flight Calculator
Find how long a Hohmann transfer takes — solve directly from the transfer orbit's semi-major axis, or build it up from your starting and target orbit radii.
How to Use This Calculator
- Pick a central body from the preset list, or choose "Custom μ."
- Basic: choose what to solve for — time of flight, semi-major axis at, or μ — and enter the other two.
- Advanced: enter your starting and target orbit radii, r₁ and r₂, and at is computed for you automatically.
- Pick a time unit — seconds, minutes, hours, or days — from the dropdown.
- Read the step-by-step solution, and in Advanced mode the orbit diagram and details, to check or show your work.
What This Tool Offers
- ✓Solve for any of three variables — time of flight, semi-major axis, or μ.
- ✓Presets for Earth, Moon, Mars, Venus, and the Sun, or a custom gravitational parameter.
- ✓Build at automatically from starting and target orbit radii in Advanced mode.
- ✓A live transfer-orbit diagram and full orbit-period breakdown in Advanced mode.
- ✓Seconds, minutes, hours, or days output, with every unit shown side by side.
What is the Hohmann transfer time of flight?
A Hohmann transfer moves a spacecraft along one half of an elliptical orbit — from the starting circular orbit to the target circular orbit. The time of flight is simply how long that half-ellipse takes to fly, which by Kepler's third law is exactly half the transfer orbit's full orbital period.
Formula
This is half of Kepler's formula for a full orbital period, T = 2π·√(a³/μ). The transfer orbit's semi-major axis is the average of the two circular orbit radii it connects: at = (r₁ + r₂) / 2.
| Symbol | Meaning |
|---|---|
| t | Time of flight — duration of the transfer, from departure burn to arrival |
| at | Semi-major axis of the transfer ellipse, (r₁ + r₂) / 2 |
| μ | Standard gravitational parameter of the central body (GM) |
| r₁, r₂ | Radii of the starting and target circular orbits, from the body's center |
Reference: gravitational parameters (μ)
| Body | μ (km³/s²) |
|---|---|
| Mercury | 22,032 |
| Venus | 324,859 |
| Earth | 398,600 |
| Moon | 4,902.8 |
| Mars | 42,828 |
| Jupiter | 126,686,534 |
| Saturn | 37,931,187 |
| Sun | 132,712,000,000 |
Reference: common orbit radii (Earth) and typical transfer times
| Transfer | r₁ → r₂ (km) | Approx. time of flight |
|---|---|---|
| LEO → ISS altitude | 6,678 → 6,798 | ≈47 minutes |
| LEO → GPS / MEO | 6,678 → 26,578 | ≈3.1 hours |
| LEO → GEO | 6,678 → 42,164 | ≈5.25 hours |
| LEO → Lunar orbit | 6,678 → 384,400 | ≈5 days |
Frequently asked questions
The spacecraft only travels from perigee to apogee of the transfer ellipse — one half of the full loop — so the time taken is exactly half of what a full orbit on that same ellipse would take.
No — the formula only depends on at, which is the same whether you're moving from r₁ to r₂ or from r₂ to r₁, so the time of flight is identical in both directions.
No — the two are independent outputs of the same transfer geometry. Δv depends on the velocity changes at each end; time of flight depends only on the transfer orbit's size (at) and μ.
Assumes an idealized two-body Hohmann transfer with impulsive burns; real mission timing must also account for launch windows and phasing.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| t | Transfer time | s |
| a_t | Transfer orbit semi-major axis | m |
| μ | Standard gravitational parameter | m3/s2 |
What it means
The Hohmann transfer time of flight is the duration of the elliptical transfer from one circular orbit to another. It equals half the period of the transfer ellipse. This formula is derived from Kepler’s third law. The time is independent of the initial and final radii except through the semi‑major axis. Mission planners use this to schedule launches (e.g., Mars launch windows). The transfer time is typically several months to years for interplanetary missions. Understanding this time is crucial for mission planning, life support, and communication windows. The formula assumes a two‑body problem and ignores gravitational perturbations.
Worked example
Hohmann Transfer Time of Flight – Two Examples
Real‑World| Parameter | Value |
|---|---|
| a_t | 2.4419×10⁷ m |
| μ | 3.986×10¹⁴ |
| Parameter | Value |
|---|---|
| a_t | 7.0×10⁶ |
Common mistakes
- Hohmann transfer time of flight: t = π · √(a_t³ / μ).
- a_t: Semi‑major axis of the transfer ellipse = (r₁+r₂)/2.
- μ: Gravitational parameter.
- Result in seconds.
- Assumes the transfer is half an ellipse.
Applications
The time of flight for a Hohmann transfer is t = π·√(a_t³/μ), where a_t is the semi‑major axis of the transfer ellipse. This gives the duration of the transfer from the inner to outer orbit (half an ellipse). Engineers use this formula to plan mission timelines, to schedule spacecraft events, and to determine the required launch windows. It is essential for interplanetary missions, where transfer times can be months or years. By calculating transfer time, aerospace engineers can coordinate with ground stations, plan thermal and power budgets, and ensure that the spacecraft arrives at the target at the correct time.
- Interplanetary mission timeline planning (Earth to Mars, etc.)
- Launch window determination and alignment
- Spacecraft system design for long‑duration cruises
- Communication and tracking schedules
- Orbit insertion and spacecraft operations coordination
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