🔺 Cone Volume Calculator 2026
Calculate volume, height, or radius of a cone
Enter Radius & Height
r = radius, h = height, l = slant
📊 Results
Base Radius (r)
5 cm
Height (h)
10 cm
Slant Height (l)
11.18 cm
Volume
261.8 cm³
Base Area
78.54 cm²
Lateral Area
175.9 cm²
📝 Step-by-Step Solution
Given: r = 5 cm, h = 10 cm
Slant height: l = √(r² + h²) = √(25 + 100) = 11.18 cm
Volume = (1/3)πr²h = (1/3)π × 25 × 10
Volume = 261.80 cm³
📐 Cone Volume Formulas
Volume: V = (1/3)πr²h
Height from Volume: h = 3V / (πr²)
Radius from Volume: r = √(3V / πh)
Slant Height: l = √(r² + h²)
Height from Slant: h = √(l² - r²)
Understanding Cone Volume
🔺 The 1/3 Factor
Cone volume is 1/3 of a cylinder with same base and height. Three cones fit exactly into one cylinder. V = (1/3)πr²h.
📏 Key Dimensions
r = base radius, h = perpendicular height (apex to base center), l = slant height (apex to base edge).
📐 Slant vs Height
Slant height ≠ height. They're related by l² = r² + h² (Pythagorean theorem). Slant is always longer than height.
🎯 Applications
Ice cream cones, funnels, party hats, traffic cones. Volume needed for filling, capacity calculations.
Frequently Asked Questions
What is the volume formula for a cone?
V = (1/3)πr²h. One-third of pi times radius squared times height.
The 1/3 factor because a cone is 1/3 of a cylinder.
Why is cone volume 1/3 of a cylinder?
Geometry principle. If you pour water from a cone into a cylinder
(same base, same height), you need exactly 3 cones to fill it.
How do I find height from volume?
h = 3V / (πr²). Rearrange the formula. Multiply volume by 3,
divide by π and radius squared.
How do I find radius from volume?
r = √(3V / πh). Take cube of (3 × volume) divided by (π × height),
then square root.
What is slant height?
Distance from apex to base edge. Measured along the cone's
surface. Related to height: l = √(r² + h²).
How do I calculate height from slant height?
h = √(l² - r²). Using Pythagorean theorem. Slant height squared
minus radius squared, then square root.
What is the base area of a cone?
A = πr². The circular base. Same as any circle with radius r.
What is lateral surface area?
A = πrl. The curved surface (not including base). Uses slant
height l, not vertical height h.
How is cone volume related to pyramid volume?
Same principle: V = (1/3) × base area × height. For pyramid, base
is polygon; for cone, base is circle.
What units should I use?
Consistent units. If radius is cm, height must be cm. Volume will
be cm³. Convert before calculating.
How do I convert volume to liters?
1 liter = 1000 cm³. Also: 1 liter = 0.001 m³. Divide cm³ by 1000
to get liters.
What is the difference between right and oblique cone?
Right cone: apex directly above center. Oblique:
apex offset. Volume formula works for both if h is perpendicular height.
Can I use diameter instead of radius?
Yes, divide by 2. If given diameter d, then r = d/2. Use radius in
the formula.
What are real-world cone examples?
Ice cream cones, traffic cones, funnels, party hats, volcanoes, pine trees
(approximate). Volume calculations for capacity.
How accurate is this calculator?
Mathematically exact for perfect cones. Uses π to full precision.
Real cones may vary slightly.
What happens if r = 0?
Volume = 0. A cone with zero radius has no base, so no volume.
Similarly, h = 0 gives zero volume.
How does doubling dimensions affect volume?
Volume increases 8×. V ∝ r²h, so doubling both gives (2)² × 2 = 8.
Doubling just r: 4×. Doubling just h: 2×.