Volume of Cone Calculator
Compute volume of a right circular cone instantly. Enter radius and height to get results, steps, and equation preview clearly.
Equation Preview
Helping Notes
Use the standard formula V = (1/3)πr²h; ensure both inputs share the same unit.
For slant height problems, convert to r and h first using Pythagoras, then apply the volume formula.
Results
Inputs Used
Volume
Base Area
Step-by-Step Substitution
Quick Check
What Is a Volume of Cone Calculator?
The Volume of Cone Calculator determines the three‑dimensional space enclosed by a right or oblique circular cone. You enter a radius (or diameter ) and a perpendicular height . The calculator sets up and evaluates the exact formula , returning both symbolic and numerical answers. It also rearranges the relation to solve for any missing variable—radius, height, or diameter—given the other two. For truncated cones (frustums), it uses the generalized expression that incorporates both top and bottom radii. Clear, responsive formulas and step‑by‑step substitutions help students, makers, and engineers verify results before applying them to material estimates, fluid capacity, or packaging design.
About the Volume of Cone Calculator
Cone volume depends only on the base area and perpendicular height: any cone with base radius and height —right or oblique—has volume . The tool accepts mixed units and keeps the computation in exact terms until the last step, so inputs in centimeters yield cubic centimeters, with optional conversions to liters or gallons. For convenience, it supports diameter input via , and provides inverse formulas and . Frustum calculations use , where and are the larger and smaller radii. Output includes exact forms (with ) and decimals to your chosen precision.
Cone volume:
Using diameter:
Solve for height: Solve for radius:
Frustum (truncated cone):
How to Use This Volume of Cone Calculator
- Choose calculation type: V from r, h; h from V, r; r from V, h; or frustum.
- Enter known values (use if you have diameter). Keep units consistent.
- Calculate to see the substituted formula, exact result with , and a decimal value. Optionally convert units.
- Copy the steps and results into your worksheet, report, or design notes.
Examples
- Right cone: ⇒ .
- Find height from volume: ⇒ .
- Using diameter: ⇒ .
- Frustum: ⇒ .
- Oblique cone check: same (not perpendicular slant input) ⇒ .
Formula Snippets Ready for Rendering
FAQs
Does slant height affect volume?
No. Volume depends on base radius and perpendicular height only: .
Can I enter diameter instead of radius?
Yes. Use , or the equivalent formula .
What units will the result have?
Units cube automatically (e.g., cm → cm³). You can convert to liters or gallons after calculation.
Is the formula valid for oblique cones?
Yes. As long as is the perpendicular height, the same volume formula applies.
How do I handle a truncated cone?
Use the frustum formula with both radii and the vertical height.
What if I know volume and height but not radius?
Solve and then compute any other needed dimensions.
Can I compare two cones’ capacities?
Yes—compute both volumes and compare. Doubling radius quadruples base area, so volume scales with .