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DailyCalc

Geometry Calculator

Area, perimeter, volume and surface area for common 2D shapes and 3D solids.

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Your details

Circle with its radius marked A circle with a dot at the centre and an arrow running from the centre to the edge, labelled r for radius. rradius

Result

Area
78.5398

square units

Circumference
31.4159

linear units

Let's work it out…

A = πr²

A = π × 5²

A = π × 25

A = 78.5398

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Formula — written step by step

A circle of radius 5…

A = πr²

A = π × 5²

A = π × 25

A = 78.5398 square units

r is the radius — the distance from the centre out to the edge. The unit follows your input: enter centimetres and the area comes out in square centimetres.

The formula for each shape

  • Circle

    Circle with its radius marked A circle with a dot at the centre and an arrow running from the centre to the edge, labelled r for radius. rradius

    A = πr²

    Needs the radius · answer in cm²

  • Rectangle

    Rectangle with length and width marked A rectangle with a dimension arrow along the bottom labelled length, and one down the right side labelled width. lengthwidth

    A = length × width

    Needs length and width · answer in cm²

  • Triangle

    Triangle with base and perpendicular height marked A triangle standing on a horizontal base. A dashed line drops from the apex at a right angle to the base, labelled height; the base carries a dimension arrow labelled base. heightbase

    A = ½ × base × height

    Needs the base and the perpendicular height · answer in cm²

  • Triangle from three sides

    Triangle with its three sides labelled A scalene triangle with each of its three sides labelled a, b and c. cabthree known sides

    A = √(s(s−a)(s−b)(s−c))

    Needs all three side lengths · answer in cm²

  • Trapezoid

    Trapezoid with both parallel sides and its height marked A trapezoid with the shorter parallel side a along the top, the longer parallel side b along the bottom, and a dashed perpendicular line between them labelled height. side aheightside b

    A = ((a + b) ÷ 2) × height

    Needs both parallel sides and the height · answer in cm²

  • Cube

    Cube with one side length marked A cube drawn in three dimensions with its hidden back edges dashed. A dimension arrow along the bottom front edge is labelled side. side

    V = s³

    Needs one side · answer in cm³

  • Rectangular box

    Rectangular box with length, width and height marked A rectangular box drawn in three dimensions with hidden edges dashed. Dimension arrows label the width along the front, the length running back in depth, and the height up the side. widthlengthheight

    V = length × width × height

    Needs length, width and height · answer in cm³

  • Sphere

    Sphere with its radius marked A sphere drawn as a circle with a dashed equator showing its roundness, and an arrow from the centre to the surface labelled r for radius. rradius

    V = 4/3 πr³

    Needs the radius · answer in cm³

  • Cylinder

    Cylinder with radius and height marked A cylinder seen at a slight angle. The hidden back of the base is dashed. An arrow across the top face is labelled r for radius, and a dimension arrow at the side is labelled height. rheight

    V = πr²h

    Needs the radius and the height · answer in cm³

  • Cone

    Cone with radius and height marked A cone standing on a circular base seen at a slight angle, with the hidden back of the base dashed. A dashed line runs from the tip straight down to the centre of the base, labelled height, and an arrow across the base is labelled r for radius. rheight

    V = πr²h ÷ 3

    Needs the radius and the height · answer in cm³

  • Triangular prism

    Triangular prism with base, triangle height and length marked A prism with a triangular end face, drawn in three dimensions with its hidden back edges dashed. The triangular face is labelled with its base and its perpendicular height, and a third arrow marks the length the prism runs back. triangle heightbaselength

    V = ½ × base × triangle height × length

    Needs the triangle's base and height, and the prism length · answer in cm³

A worked example

Volume of a rectangular box

Length
8 cm
Width
5 cm
Height
3 cm
  1. V = length × width × height
  2. V = 8 × 5 × 3
  3. V = 40 × 3

V = 120 cm³

The order does not matter — multiplication is commutative, so any face can be treated as the base and the remaining dimension as the depth.

Volume of a cylinder

Radius
5 cm
Height
8 cm
  1. V = πr²h
  2. V = π × 5² × 8
  3. V = π × 25 × 8
  4. V = π × 200

V = 628.3185 cm³

Squaring the radius before multiplying by the height is the step people skip. Doubling the radius quadruples the volume; doubling the height only doubles it.

Area of a triangle

Base
10 cm
Height
8 cm
  1. A = ½ × base × height
  2. A = ½ × 10 × 8
  3. A = ½ × 80

A = 40 cm²

Height means the perpendicular distance from the base to the opposite corner — not the length of a slanted side.

How to use this calculator

  1. Choose what you are measuring from the Shape menu. The drawing changes to match, so you can check you have picked the right one.
  2. Read the drawing to see what each measurement refers to — which line is the radius, which is the height.
  3. Enter every measurement the shape asks for, using the same unit throughout.
  4. The answer updates as you type; there is nothing to submit.
  5. Flat shapes return area and perimeter. Solids return volume and surface area.

Units are yours to choose

These formulas are unit-agnostic. Enter centimetres and areas come out in square centimetres; enter feet and you get square feet. The only rule is to use the same unit for every input in a single calculation.

Mixing units is the most common source of wrong answers — a cylinder with radius in centimetres and height in metres produces a volume that means nothing.

Radius, diameter, and the mistake in between

Every circular formula here takes the radius: the distance from the centre to the edge. The diameter is the full width across, and it is twice the radius. Measuring across a pipe or a tin gives you the diameter, so halve it before entering it.

Getting this wrong is expensive because the radius is squared or cubed. Entering a diameter where a radius belongs overstates a circle's area four times over, and a sphere's volume eight times over.

Area, surface area and volume

Area measures a flat region in square units. Surface area measures the total outside of a solid, also in square units — it is what you would need to paint or wrap. Volume measures the space inside, in cubic units.

Scaling reveals how they differ. Double every dimension of a solid and its surface area quadruples while its volume increases eightfold. This is why large animals have proportionally smaller surface areas and why crushed ice melts faster than a single block of the same mass.

Pi and the circular formulas

Pi is the ratio of any circle's circumference to its diameter, roughly 3.14159. Every circular and spherical formula here derives from it: circumference is 2πr, area is πr², sphere volume is 4/3 πr³.

The exponent tells you the dimension. Circumference is linear in r, area is quadratic, volume is cubic — which is why a modest increase in radius produces a dramatic increase in volume.

Every formula this calculator uses

ShapeArea or volumePerimeter or surface areaMeasurements needed
CircleA = πr²C = 2πrradius
RectangleA = l × wP = 2(l + w)length, width
TriangleA = ½ × b × h—base, height
Triangle (three sides)A = √(s(s−a)(s−b)(s−c))P = a + b + call three sides
TrapezoidA = ((a + b) ÷ 2) × h—both parallel sides, height
CubeV = s³S = 6s²side
Rectangular boxV = l × w × hS = 2(lw + lh + wh)length, width, height
SphereV = 4/3 πr³S = 4πr²radius
CylinderV = πr²hS = 2πrh + 2πr²radius, height
ConeV = πr²h ÷ 3S = πr(r + √(r² + h²))radius, height
Triangular prismV = ½ × b × h × length—triangle base and height, length

In the three-sided triangle, s is the semi-perimeter — half of a + b + c. That is Heron's formula, and it is how you find an area without knowing any height.

Squared and cubed units

ThisEquals
1 m²10,000 cm²
1 m³1,000,000 cm³
1 m³1,000 litres
1 litre1,000 cm³
1 ft²144 in²
1 ft³1,728 in³

Converting a squared unit squares the factor and a cubed unit cubes it. A metre is 100 cm, so a square metre is 100² cm² and a cubic metre 100³ cm³ — which is why converting volumes by the plain length factor is wrong by a factor of a million.

Frequently asked questions

Why does the three-sided triangle sometimes refuse to compute?

Because of the triangle inequality: any side must be shorter than the sum of the other two. Sides of 1, 2 and 10 cannot close into a triangle.

Is volume measured in square or cubic units?

Cubic. Area covers a flat surface and is measured in squared units such as cm² or ft²; volume fills a space and is measured in cubed units such as cm³ or ft³. Surface area is the total area of a solid's outside, so it goes back to squared units.

What is the difference between radius and diameter?

The radius runs from the centre to the edge; the diameter runs all the way across through the centre. The diameter is exactly twice the radius, so halve any measurement taken across a circle before entering it here.

How do I calculate the volume of a box?

Multiply length by width by height. A box 8 cm long, 5 cm wide and 3 cm high holds 8 × 5 × 3 = 120 cm³. Choose "Rectangular box" above and the drawing shows which edge each measurement refers to.

Can I use different units?

Yes, as long as every measurement in one calculation uses the same unit. Enter centimetres and you get square or cubic centimetres back; enter feet and you get square or cubic feet. What you cannot do is mix them — a cylinder with its radius in centimetres and its height in metres produces a number that means nothing. Convert one first.

Why does the triangular prism not report a surface area?

Because a base and a perpendicular height do not describe one triangle — infinitely many triangles share them, and each has different sloping sides. Volume only needs the cross-sectional area, so it is well defined; the total surface area is not, and reporting one would mean quietly assuming the triangle is isosceles.

How do I find the area of a triangle without knowing its height?

Choose "Triangle (three sides)" and enter the three side lengths. That uses Heron's formula, which needs no height at all — useful for a plot of land where the sides can be paced out but no perpendicular can be.

How do I find the area of an irregular shape?

Divide it into rectangles and triangles, compute each, and add them. For land in particular this is far more reliable than trying to fit a single formula.

What is the difference between a cone and a pyramid?

A cone has a circular base, a pyramid a polygonal one. Both have volume equal to one third of base area times height.