Cone lateral area
Cone lateral area S = πr·l with slant height l = √(r²+h²): enter the radius and height to get the lateral area plus slant height, base, total area and volume; values are rounded to 6 decimals and non-positive input is rejected.
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Result
One quantity per line, ready to copy.
Enter a radius to calculate
What this tool does
- Check the cone lateral area and get the slant height, base area and surface area for layout or cutting.
- Compare volume and lateral area across different cone angles to estimate material cost.
- Verify the formulas: slant √(r²+h²), lateral πr·l, total πr² + πr·l.
Example
Input
3
Output
半径 3 高 4 的圆锥侧面积：47.12389 母线 √(r²+h²)：5 底面积 πr²：28.274334 侧面积 πr·l：47.12389 全面积 πr² + πr·l：75.398224 体积 πr²h/3：37.699112 长度单位 u，面积 u²，体积 u³
At radius 1 and height 1 the slant height is √2 ≈ 1.414214, the lateral area π√2 ≈ 4.442883 and the volume π/3 ≈ 1.047198 — all matching the canonical values.
Frequently asked questions
What is the slant height?
The slant height l is the distance from the apex to any point on the base circle, l = √(r²+h²). The lateral surface unrolls into a sector whose radius is exactly the slant height, which is why it is needed for the lateral area.
Lateral vs total area?
The lateral area covers only the curved surface (πr·l); the total area adds the base circle (πr²). Use the total for a closed container and the lateral for an open cone.
What if the radius is 0?
It reports an error. With a zero radius or height the cone degenerates into a line or a disk — the formula still evaluates but the answer is meaningless, so non-positive input is rejected.
Keywords：圆锥侧面积Cone lateral area圆锥cone几何计算geometry侧面积