03 // Bidirectional STEM Calculators // MATHV = (1 / 3) × π × r² × h

Right Circular Cone Volume, Radius & Height Calculator

By Cavalieri's principle, the volume V of a right circular cone equals exactly one-third the volume of a cylinder sharing the same base radius r and perpendicular height h: V = (1/3) × π × r² × h.

V = (1 / 3) × π × r² × h

Pick which value you want to calculate (or type into any field):Solving for: V — Cone Volume

Cone VolumeCalculated

Enclosed conical volume

0.001100,000,000.00

Base Radius

Radius of the circular base

0.011,000.00

Perpendicular Height

Vertical altitude from base center to apex

0.015,000.00

Calculated Result · Cone Volume (V)

314.1593m³

Converted units:

Step-by-Step Calculation

01Canonical Law: V = (1 / 3) × π × r² × h

02Given Inputs (Base Units): r = 5 m, h = 12 m

03Solve for V (Cone Volume): V = 314.16 m³

Real-World Reference Values

Slant Height (s = √(r² + h²))At r = 5, h = 12 → s = 13

Forms a 5-12-13 Pythagorean right triangle

Lateral Conical Surface AreaA_L = π × r × √(r² + h²)

Sheet metal development area for conical hoppers

Aggregate Stockpile Angle of Reposetan(α) = h / r (typically 30°–38°)

Gravel and grain silo hopper sizing

20-Row Comparison Table

Cone Volume (V) · Base Radius (r)

Compare across:

Right Circular Cone Volume, Radius & Height Calculator — Base Radius → Cone Volume
#	Base Radius (m)	Cone Volume (m³)	Δ %
01	0.01 m	0.001257 m³	-100.00%
02	5 mCurrent	314.1593 m³	0.00%
03	15.0088 m	2,830.75 m³	+801.06%
04	22.5082 m	6,366.37 m³	+1926.48%
05	30.0076 m	11,315.47 m³	+3501.83%
06	37.507 m	17,678.06 m³	+5527.10%
07	45.0064 m	25,454.15 m³	+8002.31%
08	52.5058 m	34,643.72 m³	+10927.44%
09	60.0052 m	45,246.79 m³	+14302.50%
10	67.5046 m	57,263.35 m³	+18127.49%
11	75.004 m	70,693.40 m³	+22402.41%
12	82.5034 m	85,536.94 m³	+27127.25%
13	90.0028 m	101,793.97 m³	+32302.03%
14	97.5022 m	119,464.49 m³	+37926.73%
15	105.0016 m	138,548.51 m³	+44001.36%
16	112.501 m	159,046.01 m³	+50525.92%
17	120.0004 m	180,957.01 m³	+57500.40%
18	127.4998 m	204,281.49 m³	+64924.82%
19	134.9992 m	229,019.47 m³	+72799.16%
20	142.4986 m	255,170.94 m³	+81123.43%

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Frequently Asked Questions

How is slant height s calculated from base radius r and height h?+

The radius r, vertical height h, and slant height s form a right triangle, so s = √(r² + h²).

Why is there a factor of 1/3 in every cone and pyramid volume formula?+

Integrating cross-sectional area A(z) = A_base × (z / h)² from z = 0 to h yields ∫ u² du = 1/3 regardless of base shape.

How do I size a conical grain hopper for a target volume?+

Click SOLVE FOR on h (or r) and enter your target storage volume V.