Introduction
A cone is a 3D shape with a circular base that narrows to a point at the top, called the apex. Think of an ice cream cone or a party hat. The volume of a cone tells you how much space is inside it. To find the volume, you need two measurements: the radius of the circular base and the height of the cone. The formula is V = (1/3) × π × r² × h, where r is the radius and h is the height. This means a cone holds exactly one-third the volume of a cylinder with the same base and height. Use this Cone Volume Calculator to get your answer quickly — just enter the radius and height, and the tool does the math for you.
How to Use Our Cone Volume Calculator
Enter the dimensions of your cone, and this calculator will find the volume, surface area, slant height, and other key measurements. It works for right cones, oblique cones, and truncated cones (frustums).
Cone Type: Pick the type of cone you want to calculate. Choose "Right Cone" for a standard cone with the tip centered over the base, "Oblique Cone" for a tilted cone where the tip is off-center, or "Truncated Cone (Frustum)" for a cone with the top cut off flat.
I Know: Select which two or three measurements you already have. For example, with a right cone you can enter radius and height, radius and slant height, radius and volume, or several other combinations. The calculator will solve for all the missing values based on what you provide.
Radius (r) or Base Radius (R): Enter the distance from the center of the circular base to its edge. For a truncated cone, this is the radius of the larger bottom circle.
Top Radius (r) — Truncated Cone Only: Enter the radius of the smaller top circle on a truncated cone.
Height (h): Enter the straight-up-and-down distance from the base to the tip of the cone. For an oblique cone, this is the perpendicular height, not the slant distance.
Slant Height (s): Enter the distance along the sloped side from the base edge to the tip. This value must be larger than both the radius and the height for a right cone.
Volume (V), Lateral Surface Area (L), or Total Surface Area (A): If you already know one of these values instead of a length measurement, enter it here. The calculator will work backward to find the missing dimensions.
Output Length Unit: Choose the unit of measurement for your results. Options include meters, centimeters, millimeters, inches, feet, and yards. All outputs, including the volume conversion table, will update to match your selection.
After entering your values, click "Calculate" to see the full results. You will get the volume, lateral surface area, base surface area, total surface area, slant height, radius, and height — all displayed as decimal values and in terms of π. A surface area breakdown chart and a volume unit conversion table are also provided below the results.
Cone Volume Calculator
A cone is a three-dimensional shape with a flat circular base that tapers smoothly to a single point called the apex. Think of an ice cream cone or a party hat. This calculator helps you find the volume, surface area, slant height, and other properties of a cone using the measurements you already know.
What Is the Volume of a Cone?
The volume of a cone tells you how much space is inside it. The formula for the volume of a cone is:
V = (1/3)πr²h
In this formula, r is the radius of the circular base, h is the height (measured straight up from the base to the tip), and π (pi) is approximately 3.14159. The volume of a cone is exactly one-third the volume of a cylinder with the same base and height. That means if you filled a cone with water three times, it would fill the matching cylinder completely.
Types of Cones
This calculator supports three types of cones:
- Right Cone – The most common type. The apex sits directly above the center of the base. The height drops straight down at a 90-degree angle to the base. You can calculate volume, slant height, lateral surface area, base area, and total surface area for this type.
- Oblique Cone – The apex is not centered above the base, so the cone leans to one side. The volume formula is the same as a right cone, but you must use the perpendicular height (the shortest vertical distance from the base to the apex), not the length of the tilted side. Surface area formulas do not apply to oblique cones because their curved surface is not uniform.
- Truncated Cone (Frustum) – A cone with the top cut off by a flat plane parallel to the base. This creates two circular faces: a larger base with radius R and a smaller top with radius r. The volume formula is V = (1/3)πh(R² + Rr + r²). Frustums appear in everyday objects like buckets, lampshades, and drinking cups.
Key Cone Measurements
- Radius (r) – The distance from the center of the circular base to its edge.
- Height (h) – The perpendicular distance from the base to the apex.
- Slant Height (s) – The distance along the surface from the base edge to the apex. For a right cone, you can find it using the Pythagorean theorem: s = √(r² + h²). This is the same relationship used in a right triangle, where the radius, height, and slant height form the three sides.
- Lateral Surface Area – The area of the curved surface only, not including the base. For a right cone: L = πrs.
- Total Surface Area – The lateral surface area plus the area of the base. For a right cone: A = πr(r + s). The base itself is a circle, so its area is πr², which you can also compute with our Circle Area Calculator.
How to Use This Calculator
First, select the type of cone you are working with. Then choose which two measurements you already know (or three, for a truncated cone). Enter your values, pick your preferred unit of measurement, and the calculator will solve for every remaining property. It also shows results in terms of π, gives you a detailed breakdown table, displays the formulas used, and converts the volume into multiple units automatically.
Practical Uses
Cone volume calculations come up in many real-world situations. Engineers use them when designing funnels, silos, and rocket nose cones. Construction workers calculate cone volumes for sand or gravel piles — if you're working with bulk materials, tools like a Gravel Calculator or Sand Calculator can also help estimate quantities. Chefs and food manufacturers need cone measurements for molds and packaging. Students encounter cone problems regularly in geometry and calculus classes. If you need to find the volume of other 3D shapes, try our Sphere Volume Calculator or Cylinder Volume Calculator. For related area calculations, you may also find the Triangle Area Calculator and Square Footage Calculator helpful. Knowing how to find the volume of a cone is a basic but important math skill that applies across many fields.