Frustum Volume Calculator

Geometry

Truncated cone volume, slant height and surface area

Quick Answer

Frustum Volume Calculator: Truncated cone volume, slant height and surface area. Volume: V = πh(R² + Rr + r²) / 3.

Enter any one value, the rest auto-solve

Lower radius R

Upper radius r

Height h

Slant height sauto

Volume Vauto

Lateral area Slauto

Diagram (updates live with input)

Step-by-step

s = √(h² + (R − r)²) = √(6.0000² + 3.0000²) = 6.7082

V = πh(R² + Rr + r²)/3 = π × 6.0000 × 129.0000 / 3 = 810.5309

侧面积 = π(R + r)s = π × 13.0000 × 6.7082 = 273.9678

表面积 = 侧面积 + π(R² + r²) = 553.5695

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How to Use

Enter known values: fill sides, radius or angles in the Frustum Volume Calculator.
Auto-solve the rest: all unknowns are solved instantly — no manual derivation.
See formula and steps: the result panel shows the formula used and the substitution.
Try another case: change any known value to solve again.

Key Points

Frustum Volume Calculator is a free online geometry tool — open and use, no sign-up.
All calculations run locally in your browser; your data never leaves the device.
Key capability: Truncated cone volume, slant height and surface area.
Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Frustum (truncated cone) math

Volume: V = πh(R² + Rr + r²) / 3

Slant height: l = √(h² + (R−r)²)

Lateral area: π(R + r)l; total adds πR² + πr²

r=0 degenerates to a cone: V = πR²h/3

Example: bucket R=15, r=10, h=30 cm → V = 4750π ≈ 14.92 L; l ≈ 30.4 cm; lateral ≈ 2388 cm².

FAQ

How do I use the Frustum Volume Calculator?

Open the page and fill in the input fields — results update automatically. Truncated cone volume, slant height and surface area.

Are the results accurate?

Yes. Standard formulas and conversion factors are used and verified.

Is it free? Do I need to sign up?

Completely free. No registration, login or download required.

Does it work on mobile?

Yes. The responsive design works on phones, tablets and desktops.

Is my data saved?

No. Everything runs locally in your browser.

Related Guides

Source & Updates

Based on standard Euclidean geometry formulas. Last updated: 2025-07

Last updated: 2026-08-07

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Cite this page: YiJianSuan. Frustum Volume Calculator[EB/OL]. https://www.yijiansuan.com/en/c/geometry/frustum

Results provided by this tool are for reference only and do not constitute professional advice.