Orbital Eccentricity Calculator
Orbital eccentricity is the single number that captures how stretched an orbit is. A value of zero means a perfect circle, while values rising toward one describe progressively more elongated ellipses. This calculator computes eccentricity from the two extreme points of an orbit: the apoapsis, the farthest distance from the central body, and the periapsis, the closest distance. The formula is eccentricity equals apoapsis minus periapsis, divided by their sum. You enter the two distances in any consistent unit, kilometers, astronomical units or miles, and the tool returns the eccentricity, computed deterministically from the formula shown below, never estimated, so the worked example reconciles exactly with the figure on screen. Because the result depends only on the ratio of the distances, the choice of unit does not matter as long as both use the same one. Eccentricity is one of the orbital elements that, together with the semi-major axis and the orientation angles, specify an orbit in Kepler's framework. Earth's orbit is nearly circular at about 0.0167, while comets often exceed 0.9, swooping far out before diving close to the Sun. Use this tool to characterize a planet, moon or spacecraft orbit, or to check an orbital mechanics problem.
Orbital eccentricity is e = (ra - rp) / (ra + rp), where ra is apoapsis and rp is periapsis. For Earth's orbit with apoapsis 152,100,000 km and periapsis 147,100,000 km, the eccentricity is 0.0167.
Orbital eccentricity formula
e = (ra - rp) / (ra + rp)
ra = apoapsis distance (farthest point)
rp = periapsis distance (closest point)
0 = circle, near 1 = highly elongated ellipse
Eccentricity is the difference between the farthest and closest distances divided by their sum. For any bound elliptical orbit the numerator is smaller than the denominator, so the result is a number between 0 and 1.
Worked example
Earth's apoapsis is about 152,100,000 km and its periapsis about 147,100,000 km.
- ra - rp = 152,100,000 - 147,100,000 = 5,000,000
- ra + rp = 152,100,000 + 147,100,000 = 299,200,000
- e = 5,000,000 / 299,200,000 = 0.0167
Earth's orbital eccentricity is about 0.0167, a nearly circular orbit. These are the calculator's default inputs, so the result above matches the widget exactly.
Eccentricity of selected orbits
| Body | Eccentricity (approx.) |
|---|---|
| Venus | 0.0068 |
| Earth | 0.0167 |
| Mars | 0.0934 |
| Mercury | 0.2056 |
| Halley's Comet | 0.9671 |
Reference: US National Aeronautics and Space Administration (NASA).
Orbital eccentricity: frequently asked questions
What is orbital eccentricity?
Orbital eccentricity is a number from 0 to just under 1 that describes how stretched an elliptical orbit is. An eccentricity of 0 is a perfect circle, while values approaching 1 are highly elongated ellipses. It is one of the basic parameters astronomers use to describe the shape of a planet, moon or comet orbit.
What are apoapsis and periapsis?
Apoapsis is the farthest point of an orbit from the body being orbited, and periapsis is the closest point. Around the Sun these are aphelion and perihelion; around Earth they are apogee and perigee. The eccentricity is computed from the distances at these two extreme points.
What is the eccentricity formula?
Eccentricity equals the apoapsis distance minus the periapsis distance, divided by their sum: e = (ra - rp) / (ra + rp). Because the numerator is always smaller than the denominator for a bound orbit, the result lies between 0 and 1.
What does Earth's eccentricity tell us?
Earth's orbit has an eccentricity of about 0.0167, very nearly circular. This small value is why the Sun's distance and the seasons change only modestly over the year. Comets, by contrast, often have eccentricities above 0.9, swinging far out and then plunging close to the Sun.
What happens at eccentricity 1 or above?
An eccentricity of exactly 1 is a parabolic trajectory, and values above 1 are hyperbolic, both unbound paths that escape rather than orbit. The formula here applies to closed elliptical orbits, where apoapsis and periapsis are both finite, giving an eccentricity below 1.
Official sources
- Orbital mechanics and planetary data reference: US National Aeronautics and Space Administration (NASA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.