A = πab
Area
Area equals pi times the semi-major axis times the semi-minor axis.
NUT ENGINEERING TOOLS
Ellipse Solver
See It. Solve It. Understand It.
Enter two independent ellipse measurements. Nut solves the remaining geometry and shows how the axes, focal distance, eccentricity, area, and perimeter relate.
Live Geometry
Diagram updates to show the solved ellipse proportions.
Enter What You Know
Enter two independent measurements. Leave unknown values blank.
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Calculated Results
Complete ellipse geometry from the measurements entered.
Semi-Major Axis (a)
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Semi-Minor Axis (b)
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Major Axis
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Minor Axis
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Area
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Focal Distance (c)
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Eccentricity (e)
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Approx. Perimeter
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Your Solution
Nut shows the equations and values used to solve the ellipse.
Enter two independent measurements and solve the ellipse to see the steps.
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How It Works
Ellipse geometry is defined by its semi-major and semi-minor axes.
c = √(a² − b²)
Focal Distance
Focal distance is measured from the center of the ellipse to either focus.
e = c ÷ a
Eccentricity
Eccentricity describes how elongated the ellipse is. A circle has eccentricity zero.
Major = 2a
Major Axis
The major axis is twice the semi-major axis.
Minor = 2b
Minor Axis
The minor axis is twice the semi-minor axis.
P ≈ π(a+b)[1 + 3h/(10+√(4−3h))]
Approximate Perimeter
Nut uses Ramanujan's second approximation for a highly accurate ellipse perimeter.
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