圆形与椭圆计算器
指导
圆形与椭圆计算器
Calculate all properties of circles and ellipses instantly. Enter any single known measurement — radius, diameter, circumference, or area — and get every other circle property derived automatically. For ellipses, enter the semi-major and semi-minor axes to get area, perimeter (Ramanujan approximation), eccentricity, and foci distance. Includes a visual canvas diagram with labeled measurements and sector/segment calculations for circles.
如何使用
Select either 圆形 或者 椭圆 mode. Choose your preferred unit of measurement and decimal precision. For circles, pick which value you know (radius, diameter, circumference, or area), enter it, and all other properties calculate instantly. Optionally enter a sector angle to compute arc length and sector area. For ellipses, enter the semi-major and semi-minor axis lengths to see area, perimeter, eccentricity, foci distance, and a labeled diagram.
特征
- Circle Solver – Solve from any input: radius, diameter, circumference, or area
- Ellipse Calculator – Area, perimeter (Ramanujan approximation), eccentricity, foci distance, and semi-latus rectum
- Sector & Segment – Arc length and sector area for any angle (0-360°)
- 单位选择器 – Supports mm, cm, m, inches, feet, and yards
- Visual Diagram – Canvas-based diagram with labeled measurements, foci points, and sector highlighting
- 可调节精度 – Choose 0 to 10 decimal places
- 复制结果 – One-click copy of all calculated values
常问问题
-
Ramanujan对椭圆周长的近似公式是什么？
The Ramanujan approximation estimates the perimeter of an ellipse using the formula: P ≈ π[3(a+b) - √((3a+b)(a+3b))], where a and b are the semi-major and semi-minor axes. It is one of the most accurate simple approximations available, with error less than 0.04% for most ellipses.
-
How is eccentricity of an ellipse calculated and what does it mean?
Eccentricity (e) is calculated as e = √(1 - b²/a²), where a is the semi-major axis and b is the semi-minor axis. It measures how much the ellipse deviates from a perfect circle. A value of 0 means a perfect circle, while values approaching 1 indicate a very elongated ellipse.
-
What is the relationship between a circle and an ellipse?
A circle is a special case of an ellipse where both semi-axes are equal (a = b = radius). All formulas for ellipses reduce to the standard circle formulas when a equals b. For example, the ellipse area formula πab becomes πr² when a = b = r.
-
What are the foci of an ellipse and why are they important?
The foci (plural of focus) are two special points inside an ellipse. The sum of distances from any point on the ellipse to both foci is constant and equals the length of the major axis (2a). The distance from the center to each focus is c = √(a² - b²). Foci are fundamental in optics, astronomy (planetary orbits are ellipses with the sun at one focus), and engineering.
