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Slant Height of Cone Calculator.

Calculate cone slant height and lateral surface area.

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Set your values

Results update as you type.

Result: slantHeight: 5.00000000 · lateralArea: 47.12388980

Result

slantHeight: 5.00000000 · lateralArea: 47.12388980

Use Cases

Math homework and geometry problems

Quickly verify slant height and lateral area calculations for school assignments or exam prep.

Example: Find the slant height of a cone with radius 3 cm and height 4 cm.

Design and construction projects

Determine the slant height for making cones from sheet metal, paper, or other materials, and estimate the lateral surface area.

Example: Calculate the lateral area of a cone-shaped lampshade with given dimensions.

Frequently Asked Questions

What is the slant height of a cone?
The slant height is the distance from the apex (tip) of the cone down to a point on the edge of the base, measured along the curved surface. It forms the hypotenuse of a right triangle with the radius and height.
How is the slant height calculated?
The slant height (l) is calculated using the Pythagorean theorem: l = √(r² + h²), where r is the radius of the base and h is the height of the cone. This calculator uses that formula.
What is the lateral area of a cone?
The lateral area is the surface area of the cone's curved side, excluding the base. It is calculated as π * r * l, where r is the radius and l is the slant height. This calculator provides that value.

Tips & Common Mistakes

Tips

  • Ensure both radius and height are in the same units before calculating.
  • The slant height is always greater than the radius and height individually.
  • Use the lateral area result to estimate material needed for a cone-shaped surface.
  • Double-check your inputs: a negative radius or height is not valid.

Common Mistakes to Avoid

  • Confusing slant height with the height of the cone; they are different.
  • Forgetting to square the radius and height before adding them.
  • Using diameter instead of radius; the calculator expects the radius value.

Last updated: August 13, 2026