Circle & Ellipse Calculator
مرشد
Circle & Ellipse Calculator
Calculate all properties of circles and ellipses from any known measurement. In circle mode, enter any single value — radius, diameter, circumference, or area — and get all other measurements instantly, plus sector and segment calculations for any angle. In ellipse mode, enter the semi-major and semi-minor axes to get area, perimeter (Ramanujan approximation), eccentricity, foci distance, and more. Both modes include interactive canvas diagrams with labeled measurements.
كيف تستعمل
Switch between Circle and Ellipse mode using the tabs. For circles, enter any known value and all other properties auto-calculate. Optionally enter a sector angle to calculate arc length and sector area. For ellipses, enter the semi-major axis (a) and semi-minor axis (b) to get all properties. Select your preferred unit from millimeters to yards, adjust decimal precision, and copy all results with one click. The canvas diagram updates in real time as you type.
سمات
- Circle Mode – Solve from radius, diameter, circumference, or area. Any single input derives all other measurements
- Ellipse Mode – Calculate area, perimeter (Ramanujan approximation), eccentricity, foci distance, and semi-latus rectum from semi-axes
- Sector & Segment Calculator – Enter an angle in degrees to get arc length and sector area for circles
- Canvas Diagrams – Interactive visual diagrams with labeled measurements for both circles and ellipses, including foci markers
- Unit Selector – Millimeters, centimeters, meters, inches, feet, and yards
- Formula Reference – All formulas displayed for educational value
- دقة قابلة للتكوين – اضبط المنازل العشرية من 0 إلى 10
- Copy All Results – Copy every calculated value to clipboard in one click
التعليمات
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How do you calculate the circumference of a circle from its area?
First find the radius from the area using r = sqrt(A / pi), then calculate circumference with C = 2 * pi * r. For example, a circle with area 100 square centimeters has radius sqrt(100 / 3.14159) = 5.642 cm, giving circumference 2 * 3.14159 * 5.642 = 35.449 cm. This calculator handles these inverse calculations automatically: just enter the area and all other values appear instantly.
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What is the Ramanujan approximation for ellipse perimeter?
The Ramanujan approximation estimates an ellipse perimeter as P approximately equals pi times (3(a + b) minus the square root of (3a + b)(a + 3b)), where a and b are the semi-major and semi-minor axes. Unlike circles, there is no exact closed-form formula for an ellipse perimeter. Ramanujan published this approximation in 1914, and it is accurate to within 0.01% for most ellipses. For highly eccentric ellipses (very elongated), more complex series expansions provide better accuracy.
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What is eccentricity and what does it tell you about an ellipse?
Eccentricity measures how much an ellipse deviates from being a perfect circle. It is calculated as e = sqrt(1 - b squared / a squared), where a is the semi-major axis and b is the semi-minor axis. A circle has eccentricity 0 (a = b), while values approaching 1 indicate increasingly elongated ellipses. Earth's orbit around the Sun has an eccentricity of about 0.017, making it nearly circular. Pluto's orbit has eccentricity 0.25, noticeably more elliptical.
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What is the difference between a sector and a segment of a circle?
A sector is the pie-slice-shaped region bounded by two radii and an arc. Think of a slice of pizza. Its area equals (angle / 360) times pi times r squared. A segment is the region between a chord and the arc it cuts off. Think of cutting a circle with a straight line. A segment area equals the sector area minus the triangle formed by the two radii and the chord. This calculator computes sector area and arc length for any angle you enter.
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