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Free ellipse calculator & area calculator. Calculate ellipse area, perimeter, eccentricity, focal distance & semi-major/minor axes with formulas. Our calculator uses ellipse geometry formulas to compute area (πab), perimeter approximations, eccentricity, and focal properties for any ellipse dimensions.
Last updated: February 2, 2026
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The longest radius of the ellipse (from center to edge)
The shortest radius of the ellipse (from center to edge)
Area (A = πab):
47.1239 cm²
Formula: A = π × a × b
Perimeter (Ramanujan's approximation):
25.527 cm
Approximate circumference of the ellipse
Eccentricity (e):
0.8
e = √(1 - b²/a²) • Range: 0 (circle) to 1 (line)
Linear Eccentricity (c):
4 cm
√(a² - b²)
Focal Distance:
8 cm
Distance between foci (2c)
Semi-Major Axis (a):
5 cm
Longest radius
Semi-Minor Axis (b):
3 cm
Shortest radius
Ellipse Formulas:
Ellipse Properties:
Formula
A = πab
Calculate the enclosed area of the ellipse
Ramanujan's Formula
P ≈ π(a + b)(1 + 3h/...)
Highly accurate perimeter approximation
Formula
e = √(1 - b²/a²)
Ranges from 0 (circle) to 1 (line)
Formula
2c = 2√(a² - b²)
Distance between the two focal points
Axes
a ≥ b
Major axis (longest) and minor axis (shortest)
Multiple Methods
Various Approximations
Accurate perimeter calculations using approximations
Ellipse with semi-major axis a = 5 cm, semi-minor axis b = 3 cm
Area
47.12 cm²
π × 5 × 3
Perimeter
25.53 cm
Ramanujan approx.
Eccentricity
0.8
√(1 - 9/25)
Focal Distance
8 cm
2√(25 - 9)
Our ellipse calculator computes all geometric properties of an ellipse from the semi-major and semi-minor axes. The calculator uses fundamental ellipse formulas including Ramanujan's approximation for perimeter, which provides accuracy within 0.1% for most ellipses.
Area:
A = πabwhere a = semi-major axis, b = semi-minor axis
Eccentricity:
e = √(1 - b²/a²)measures elongation (0 = circle, 1 = line)
Linear Eccentricity:
c = √(a² - b²)distance from center to each focus
Perimeter (Ramanujan):
P ≈ π(a + b)(1 + 3h/(10 + √(4 - 3h)))where h = (a - b)²/(a + b)²
The ellipse has two foci located at (±c, 0) along the major axis. The defining property of an ellipse is that the sum of distances from any point on the curve to both foci is constant and equals 2a.
Shows semi-major axis, semi-minor axis, and focal points
An ellipse is a conic section—the intersection of a cone with a plane at an angle to its base. The standard equation is (x²/a²) + (y²/b²) = 1. The ellipse is one of the most important curves in mathematics and physics, appearing in planetary orbits (Kepler's First Law), optics, acoustics, and many engineering applications.
Need help with other conic sections? Check out our parabola calculator and area of sector calculator.
Get Custom Calculator for Your PlatformResults Summary:
Area: 75.40 cm²
Perimeter: 31.87 cm
Eccentricity: 0.745
Focal Distance: 8.94 cm
When a = b = 5 cm
Area = π × 25 = 78.54 cm², e = 0 (circle)
When a = 10 cm, b = 2 cm
Area = 62.83 cm², e = 0.98 (very elongated)
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