Cone Calculator

Free Online Cone Calculator

This cone calculator helps you instantly find the radius, diameter, height, slant height, volume, curved surface area, and total surface area of any right circular cone from just two known values. Simply choose a combination — radius and height, diameter and height, volume and radius, or volume and height — and the calculator solves for every other value automatically, complete with a shaded 3D diagram and a full step-by-step solution that shows exactly how each formula was applied.

Whether you're a student solving mensuration problems, a teacher preparing worked examples for class, an engineer designing a hopper or funnel, or simply someone searching online for a fast and accurate volume of a cone calculator or surface area of a cone calculator, this tool covers every common cone calculation you're likely to need in seconds.

A cone is a three-dimensional solid with a single flat circular base that tapers smoothly to a point called the apex. Because a right circular cone is defined entirely by its radius (or diameter) and its height, knowing any two of its core measurements — radius, height, volume, or surface area — is enough for this calculator to work out every other property automatically, including the slant height.

Cone Formulas Used

A right circular cone is defined by its radius 'r' and height 'h'. Every other measurement, including the slant height, can be derived using the following standard mensuration formulas, which this calculator applies automatically:

• Slant Height: l = √(r² + h²) (using the Pythagorean theorem on the radius and height)
• Volume: V = (1/3)πr²h (one-third times pi times the radius squared times the height)
• Curved Surface Area (CSA): πrl (pi times the radius times the slant height)
• Total Surface Area (TSA): πr(r + l) (the curved surface area plus the circular base)
• Diameter: d = 2r (the diameter is always twice the radius)
• Radius from diameter: r = d / 2
• Height from volume and radius: h = 3V / (πr²)
• Radius from volume and height: r = √(3V / (πh))

How to Use This Cone Calculator

Using this calculator only takes three simple steps. First, select which pair of measurements you already know from the dropdown menu — radius & height, diameter & height, volume & radius, or volume & height. Second, type in both values you have. Third, read off the results: the calculator instantly displays the radius, diameter, height, slant height, volume, curved surface area, and total surface area, along with a to-scale shaded diagram and a detailed breakdown of the math behind every number.

This flexible 'solve from any two values' approach means you never have to manually rearrange the volume or surface area formula yourself — the calculator handles all of the algebra, including square roots and the Pythagorean theorem for slant height, no matter which pair of values you start with. It's especially useful when working backward, for example when you know how much material a conical hopper should hold and its radius, and need to find the required height, or when you know the volume and height and need the radius for manufacturing a funnel.

Worked Example

Suppose you're designing a conical funnel with a radius of 3 meters and a height of 4 meters. Enter these two values, and the calculator first computes the slant height using l = √(r² + h²) = √(9 + 16) = 5 meters. It then finds the volume using V = (1/3)πr²h ≈ 37.7 cubic meters, the curved surface area using CSA = πrl ≈ 47.12 square meters, and the total surface area using TSA = πr(r + l) ≈ 75.4 square meters — telling you exactly how much material would be needed to build the funnel, including its circular base.

This same process works in reverse for any of the four input combinations, making the tool equally useful as a radius calculator, a height calculator, a volume calculator, or a surface area of a cone calculator.

Understanding the Cone Diagram

The diagram above shades the cone body with a horizontal gradient — lighter on the left and darker on the right — to give the flat triangle a realistic curved, 3D appearance rather than looking like a plain triangle. A shaded ellipse at the base represents the circular bottom, just like looking at an ice-cream cone or party hat from a slight angle. The solid slant line from the apex to the base edge, the dashed teal vertical height line, the solid radius line, and the dashed pink diameter line are all labeled directly on the diagram with their exact calculated values, so every measurement is visible at a glance without needing to read a separate table.

Cone vs. Cylinder: What's the Difference?

A cone and a cylinder are closely related three-dimensional shapes that both have a circular base and a height, but a cylinder has two identical circular bases connected by a straight curved surface, while a cone has only one circular base that tapers to a single point at the apex. This is exactly why the volume of a cone (V = (1/3)πr²h) is always exactly one-third the volume of a cylinder with the same base radius and height. If you're working with a shape that has two equal circular ends instead of a tapering point, use our Cylinder Calculator instead.

Where Cone Calculations Are Used

Cone geometry and mensuration formulas show up constantly in real life and across many fields of study and industry:

• Students and teachers use it for geometry and mensuration homework, competitive exams, and lesson planning.
• Engineers and architects use cone volume and surface area when designing hoppers, funnels, silos, and conical roofs.
• Manufacturing industries calculate cone surface area to determine how much material, metal sheet, or fabric is needed for traffic cones, party hats, and paper cups.
• Construction and civil engineering use cone volume formulas to estimate material for conical stockpiles of sand, gravel, or grain.
• Everyday applications include calculating the capacity of ice-cream cones, funnels, and conical containers.