Cone Calculator (V = ⅓πr²h)
Cone volume, slant height and surface: V = ⅓πr²h, l = √(r²+h²), A = πr(r+l).
- Example: r = 3, h = 4 ft → V = 37.70 ft³, l = 5 ft.
Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.
How the Cone Calculator Works
The cone is one third of its bounding cylinder; slant height comes from Pythagoras and drives the lateral surface. Worked example: r = 3 ft, h = 4 ft → V = ⅓π × 9 × 4 = 37.70 ft³, l = √(9+16) = 5 ft, lateral A = πrl = 47.12 ft², total A = π × 3 × (3+5) = 75.40 ft².
- 1
Enter radius and height
Perpendicular height h, same units as r.
- 2
Calculate
Volume, slant, lateral and total area together.
- 3
Convert units if needed
ft³ ↔ gallons, m³ ↔ liters.
Use Cases
Traffic cones, hoppers and funnels capacity
Ice cream cone and waffle sizing
Roof spires and conical caps material
Snow-cone syrup and batch volumes
Tips
- 1
l² = r² + h² links all three cone dimensions
- 2
Lateral surface unrolls to a sector of radius l
- 3
⅓ appears because a cone packs three-to-a-cylinder
Common Mistakes
Using slant height l as the height h in V = ⅓πr²h
Forgetting the ⅓ factor (getting cylinder volume)
Radius/diameter mix-ups
Adding base twice in total area
FAQs
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