Enter a cone's radius and height to calculate its volume, slant height, lateral surface area, base area, and total surface area. The Cone Calculator also shows the apex angle and base angle so you get a complete geometric profile in one step.
Volume (V)
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Slant Height (s)
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Lateral Surface Area (L)
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Base Area (B)
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Total Surface Area (A)
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Half-Apex Angle (θ)
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Base Angle (β)
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A right circular cone is a three-dimensional shape with a circular base and a pointed apex (vertex) directly above the center of the base. The term 'right' means the axis from the apex to the center of the base is perpendicular to the base. This is the most common type of cone used in geometry.
The volume of a cone is calculated using the formula V = (1/3) × π × r² × h, where r is the base radius and h is the perpendicular height. This is exactly one-third of the volume of a cylinder with the same base and height.
The slant height (s) is the distance measured along the surface of the cone from the apex down to the edge of the base circle. The height (h) is the straight perpendicular distance from the apex to the center of the base. They are related by the Pythagorean theorem: s = √(r² + h²).
The lateral surface area (L) covers only the sloped side of the cone — calculated as L = π × r × s. The total surface area (A) includes the lateral area plus the circular base area (B = π × r²), giving A = π × r × (r + s). Use total surface area when you need to cover the entire cone including its base.
The half-apex angle (θ) is the angle between the central axis and any slant side of the cone, calculated as θ = arctan(r / h). The base angle (β) is the angle between the slant side and the base of the cone, calculated as β = arctan(h / r). These two angles are complementary, meaning θ + β = 90°.
The calculator works with any consistent unit of length — centimeters, meters, inches, etc. Just make sure both the radius and height are entered in the same unit. The volume result will be in cubic units and surface areas in square units of whatever length unit you used.
No — this calculator is designed for a complete right circular cone with a single apex point. A truncated cone (frustum) has two circular bases of different radii and requires different formulas. You would need a dedicated frustum or truncated cone calculator for that shape.
The total surface area is A = π × r² + π × r × s, where r is the radius and s is the slant height. This can be factored as A = π × r × (r + s). The first term (π × r²) is the base and the second term (π × r × s) is the lateral surface.