Cone Calculator
Volume, surface area, and slant height from radius and height
By Drew Budwin · Last updated July 2026 · Methodology
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Volume
Measurements
Slant Height
Base Area
Lateral Surface Area
Total Surface Area
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Cone Calculator Formula
Volume of a cone:
V = (1/3) × π × r² × h
r = base radius, h = height
Slant height:
l = √(r² + h²)
Total surface area:
A = π × r² + π × r × l
l = slant height
How to Use This Calculator
- Enter the radius of the circular base.
- Enter the height of the cone (perpendicular distance from base to apex).
- Click Calculate to see the volume, surface area, and slant height.
Frequently Asked Questions
Why does the cone formula have a 1/3?
A cone's volume is exactly one-third of the cylinder with the same base and height (V = ⅓πr²h vs. πr²h for the cylinder). You can verify this with the cylinder volume calculator. This relationship can be proven by calculus or by Cavalieri's principle.
What is the height of a cone?
The height is the perpendicular distance from the center of the base to the apex (tip). It is not the slant height along the side of the cone. If you only know the slant height l, use h = √(l² − r²).
What units does this calculator use?
This calculator is unit-agnostic. If you enter radius in cm and height in cm, the result is in cm³. Always use the same unit for both inputs.
What is the surface area of a cone?
The total surface area is SA = πr² + πrl, where l is the slant height (l = √(r² + h²)). The first term is the base area and the second is the lateral (side) area. This calculator reports all three alongside the volume.
Does this formula work for truncated cones (frustums)?
No. A truncated cone (frustum) has the top cut off and uses a different formula: V = (πh/3)(R² + Rr + r²), where R and r are the radii of the two circular faces. This calculator is for complete cones only.
What is a right circular cone vs. an oblique cone?
A right cone has its apex directly above the center of the base. An oblique cone tilts to one side. Both use the same volume formula V = ⅓πr²h as long as h is the perpendicular height, not the slant length.
Where is cone volume used in real applications?
Funnels, ice cream cones, party hats, traffic cones, and storage hoppers are all approximate cones. A gravel pile with a 4-meter base radius and 2-meter height holds about 33.5 m³. Enter those values to verify.
How does cone volume relate to pyramid volume?
Both equal one-third times base area times height. A cone's base is a circle (A = πr²); a pyramid's base is a polygon. As the number of sides in a regular pyramid grows toward infinity, it approaches a cone. Use the pyramid calculator to explore this.