What is the formula for the volume of a cone?

(1/3) π r² h: the area of the round base, π r², times the height, divided by three. The formula line sits with the drawing and the first row underneath, The working, repeats it with your numbers in, for example (1/3) × π × 0.5² × 1.2 = 0.314159265359. That third is the whole point of a cone: a cylinder of the same radius of 0.5 m and the same height of 1.2 m holds 0.942478 m³, exactly three times as much, so a cone fills a third of the tin it stands in.

Do I type the radius or the diameter?

Either, as long as you tell the tool which. The field is a radius by default and the Measure switch beside it turns it into a diameter, which is the full width across the base and the easier one to measure on something already built. The diameter is halved before it goes into the formula: the formula line then reads (1/3) π r² h, r = d/2 and the working opens with the halving, for instance r = 20 / 2 = 10. A party hat 20 cm across and 30 cm tall is (1/3) × π × 10² × 30 = 3,141.59 cm³, which the litres row gives as 3.14159 L. Putting a diameter into the radius field by mistake gives four times too much, because the radius is squared.

I measured the sloping side. What do I type as the height?

Cone requires the perpendicular distance from the apex to the plane of the base. A slant measurement cannot be entered as that height, and this page has no slant-height solver. For a right cone with radius 5 cm and slant 13 cm, the Right Triangle Calculator can first find the 12 cm perpendicular height; this Cone preset then takes radius 5 and height 12 and returns about 314.159 cm³.

How do I get litres or gallons out of a cone?

They are already under the answer. Whatever unit you measure in, the rows list litres, US gallons and UK gallons, plus three cubic units for the scale you are working at. A paper cone of radius 3 cm and height 12 cm is 113.097 cm³, which the litres row reads as 0.113097 L. A conical hopper measured in feet, radius 2 ft and height 3 ft, is 12.5664 ft³, and the rows give 355.84 litres and 94.003 US gallons. The conversions use exact definitions: a litre is 1,000 cm³, a US gallon is 231 cubic inches and a UK gallon is 4.54609 litres.

My cone is cut off at the top. Can it do a truncated cone?

A truncated cone is a frustum, and this page has no two-radius frustum input or subtraction workflow. Cone requires the radius or diameter of one circular base and the perpendicular height to a complete apex. Do not treat the removed tip as if it were still there; that needs a different geometric model.

How big is a conical pile of gravel, sand or mulch?

A heap tipped off a truck settles into something close to a cone, so measure it across the base for the diameter and up to the peak for the height. With Measure set to Diameter, a pile 3 m across and 1.2 m high is (1/3) × π × 1.5² × 1.2 = 2.82743 m³, and the rows read 2,827.43 litres, 99.8499 cubic feet and 3.69814 cubic yards, which is how aggregate is usually sold. The arithmetic is rounded for the dimensions you type; a real heap is never a perfect cone, so read it as a close estimate of the load rather than a measurement of it.

Which units can I measure the cone in?

Metres, centimetres, feet or inches, picked on the Unit row, and the radius and the height are both typed in that same unit. The volume comes back in the cube of it, m³ from metres and in³ from inches, with litres and both gallons underneath every time. Switching the unit changes how your numbers are read rather than converting them, so 0.5 typed in metres becomes half a foot when you press ft: retype the sides in the unit you picked.

How are measurements, units and saved work handled?

Choose the measured unit before typing; changing it reinterprets bare numbers rather than converting them. Decimal and scientific numbers, complete comma groups such as 1,200, numeric fractions such as 3/4 and mixed numbers such as 2 1/2 are accepted; written unit suffixes and expressions are not. Switching radius and diameter converts the current measurement to preserve the shape. Saved strings restore without writing defaults. Deliberate edits preserve independent newer saved fields, and malformed records are left intact. Results, full tank capacity and conversions must fit the supported numeric range. The visible result summary is selectable if the clipboard is unavailable.

Cone Volume Calculator

A cone's volume is (1/3) π r² h: a third of the area of its circular base, π times the radius squared, times the height straight up from the centre of that base to the tip. Type the radius and the height and the answer appears with a labelled drawing, with the formula above it and the working, your numbers put in, as the first row below. The Measure switch takes a diameter instead when that is what you measured, and the height is the vertical one, not the slanted side. This page opens the calculator on the cone whatever shape you used last, takes metres, centimetres, feet or inches, and reads the answer out in litres, US gallons and UK gallons as well as the cube of the unit you typed in.

Cylinder · π r² h0.942478m³942.478 L · 248.976 US gal · 207.316 UK gal

Shape

Measure

Radius (m)

Height (m)

Unit

A drum, can or straight pipe: use the inner radius or diameter for capacity. Height is perpendicular to the circular end, including for an oblique cylinder; it is not a slanted axis length. The drawing is schematic. Choose the measured unit before typing; changing it reinterprets the numbers.

Result summary

Cylinder, radius 0.5 m, height 1.2 m
0.942477796077 m³
The working: π × 0.5² × 1.2 = 0.942477796077 volume, in m³
Litres: 942.477796077 L
US gallons: 248.976293692 US gal
UK gallons: 207.316132342 UK gal
Cubic feet: 33.2832892609 ft³
Cubic yards: 1.23271441707 yd³
Cubic inches: 57,513.5238428 in³

The workingvolume, in m³
π × 0.5² × 1.2 = 0.942477796077
LitresL
942.477796077
US gallonsUS gal
248.976293692
UK gallonsUK gal
207.316132342
Cubic feetft³
33.2832892609
Cubic yardsyd³
1.23271441707
Cubic inchesin³
57,513.5238428

The formula is on the stage, and the working is the first row. Every answer here is one textbook formula with your numbers put in, printed so you can check it: a cylinder is π r² h, a sphere is (4/3) π r³, a pool is length times width times the average of its two depths. The horizontal tank uses the circular-segment model with stable arithmetic for a partial fill, so half way up is exactly half and a quarter of the way up is less than a quarter, because the bottom of a circle is narrow. Conversions use exact definitions: a litre is 1,000 cm³, a US gallon is 231 cubic inches and a UK gallon is 4.54609 litres. Results are rounded; drawings are schematic. No arbitrary outlines, end caps, tapered tanks, pressure, chemical dosing, reverse dimensions, subtraction or shared surface-area result is computed here.

Common questions

What is the formula for the volume of a cone?: (1/3) π r² h: the area of the round base, π r², times the height, divided by three. The formula line sits with the drawing and the first row underneath, The working, repeats it with your numbers in, for example (1/3) × π × 0.5² × 1.2 = 0.314159265359. That third is the whole point of a cone: a cylinder of the same radius of 0.5 m and the same height of 1.2 m holds 0.942478 m³, exactly three times as much, so a cone fills a third of the tin it stands in.
Do I type the radius or the diameter?: Either, as long as you tell the tool which. The field is a radius by default and the Measure switch beside it turns it into a diameter, which is the full width across the base and the easier one to measure on something already built. The diameter is halved before it goes into the formula: the formula line then reads (1/3) π r² h, r = d/2 and the working opens with the halving, for instance r = 20 / 2 = 10. A party hat 20 cm across and 30 cm tall is (1/3) × π × 10² × 30 = 3,141.59 cm³, which the litres row gives as 3.14159 L. Putting a diameter into the radius field by mistake gives four times too much, because the radius is squared.
I measured the sloping side. What do I type as the height?: Cone requires the perpendicular distance from the apex to the plane of the base. A slant measurement cannot be entered as that height, and this page has no slant-height solver. For a right cone with radius 5 cm and slant 13 cm, the Right Triangle Calculator can first find the 12 cm perpendicular height; this Cone preset then takes radius 5 and height 12 and returns about 314.159 cm³.
How do I get litres or gallons out of a cone?: They are already under the answer. Whatever unit you measure in, the rows list litres, US gallons and UK gallons, plus three cubic units for the scale you are working at. A paper cone of radius 3 cm and height 12 cm is 113.097 cm³, which the litres row reads as 0.113097 L. A conical hopper measured in feet, radius 2 ft and height 3 ft, is 12.5664 ft³, and the rows give 355.84 litres and 94.003 US gallons. The conversions use exact definitions: a litre is 1,000 cm³, a US gallon is 231 cubic inches and a UK gallon is 4.54609 litres.
My cone is cut off at the top. Can it do a truncated cone?: A truncated cone is a frustum, and this page has no two-radius frustum input or subtraction workflow. Cone requires the radius or diameter of one circular base and the perpendicular height to a complete apex. Do not treat the removed tip as if it were still there; that needs a different geometric model.
How big is a conical pile of gravel, sand or mulch?: A heap tipped off a truck settles into something close to a cone, so measure it across the base for the diameter and up to the peak for the height. With Measure set to Diameter, a pile 3 m across and 1.2 m high is (1/3) × π × 1.5² × 1.2 = 2.82743 m³, and the rows read 2,827.43 litres, 99.8499 cubic feet and 3.69814 cubic yards, which is how aggregate is usually sold. The arithmetic is rounded for the dimensions you type; a real heap is never a perfect cone, so read it as a close estimate of the load rather than a measurement of it.
Which units can I measure the cone in?: Metres, centimetres, feet or inches, picked on the Unit row, and the radius and the height are both typed in that same unit. The volume comes back in the cube of it, m³ from metres and in³ from inches, with litres and both gallons underneath every time. Switching the unit changes how your numbers are read rather than converting them, so 0.5 typed in metres becomes half a foot when you press ft: retype the sides in the unit you picked.
How are measurements, units and saved work handled?: Choose the measured unit before typing; changing it reinterprets bare numbers rather than converting them. Decimal and scientific numbers, complete comma groups such as 1,200, numeric fractions such as 3/4 and mixed numbers such as 2 1/2 are accepted; written unit suffixes and expressions are not. Switching radius and diameter converts the current measurement to preserve the shape. Saved strings restore without writing defaults. Deliberate edits preserve independent newer saved fields, and malformed records are left intact. Results, full tank capacity and conversions must fit the supported numeric range. The visible result summary is selectable if the clipboard is unavailable.

Rounded browser arithmetic for the dimensions and ideal shapes shown; pools assume a uniform or linear depth profile. Drawings are schematic. A US gallon is 231 cubic inches and a UK gallon is 4.54609 litres.