Cone Volume Calculator
Calculate the volume and slant height of a cone from its radius and height.
Did this tool answer your question?
Thanks — this helps us improve the tool.
How to use this tool
- Enter radius and height in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your volume and the full breakdown beneath it.
Calculate cone volume = (1/3) × π × r² × h and slant height = √(r² + h²).
Formula
Volume = 1/3 π r2 h
Slant height = √(r2 + h2)
volume = (1/3) * Math.PI * r * r * h slant = Math.sqrt(r*r + h*h)
How it works
This calculator computes the volume and slant height of a right circular cone from its base radius and perpendicular height. The volume formula is one-third of the equivalent cylinder's volume. The slant height is the straight-line distance from the base edge to the apex, found using the Pythagorean theorem on the right triangle formed by the radius and vertical height.
Worked example
- Enter radius r = 3 and height h = 4.
- Volume = (1/3) × π × 3² × 4 = (1/3) × π × 36 = 12π ≈ 37.6991.
- Slant height = √(3² + 4²) = √(9 + 16) = √25 = 5.
Volume ≈ 37.6991 cubic units; Slant height = 5 units.
Common mistakes to avoid
- Forgetting the 1/3 factor; a cone holds exactly one-third the volume of a cylinder with the same base and height.
- Using slant height as the vertical height h in the volume formula; h must be the perpendicular height from base to apex.
- Confusing slant height l = sqrt(r²+h²) with lateral surface area π×r×l; slant height is a length, not an area.
Key terms
- Base radius (r)
- The radius of the circular base of the cone.
- Perpendicular height (h)
- The vertical distance from the centre of the base to the apex, measured at a right angle to the base.
- Slant height
- The distance along the sloping surface from the base edge to the apex, calculated via the Pythagorean theorem.
- Apex
- The pointed tip of the cone, located directly above the centre of the base in a right circular cone.
Frequently asked questions
- How do you calculate the volume of a cone?
- Volume = (1/3) × π × r² × h. The slant height l = √(r² + h²).