Area & Volume Calculator
Area and perimeter for twelve flat shapes, volume and surface area for twelve solids — with the formula shown, the numbers checked, and unit conversion built in.
Pick a shape
Pick a solid
Measurements
Area
The same answer in other units
| Unit | Area |
|---|
How to use this calculator
Step by step
- Choose Flat shapes for area and perimeter, or Solids for volume and surface area.
- Click a shape. The measurement boxes change to exactly the ones that shape needs, and the formula being used appears underneath them.
- Type your measurements. Everything updates as you type — there is no calculate button.
- Set the unit once, at the bottom of the measurement card. All the boxes use it, and the results are labelled in it.
- For solids, the capacity in litres and US gallons is worked out automatically — that is usually what you want from a tank, a pipe or a pond.
- The conversion table at the bottom repeats the main answer in every supported unit, so you never have to convert by hand.
Good to know
- Mixing units is the most common mistake. Convert everything to one unit before you type, or the answer will be quietly wrong.
- For a parallelogram and a trapezoid, the height means the perpendicular distance, not the length of the slanted side. Using the slant inflates the area.
- Any awkward room can be broken into rectangles and triangles, worked out separately and added. The L-shape entry does the two-rectangle version for you.
- One cubic metre is exactly 1000 litres. That single fact converts most tank and pond problems in your head.
- Doubling every dimension of a solid multiplies its surface area by 4 and its volume by 8. That is why large containers are more material-efficient than small ones.
- The ellipse perimeter and the ellipsoid surface area are approximations — no exact elementary formula exists for either. Both are well within a percent.
The maths behind it
- Rectangle A = wh, P = 2(w + h)
- Circle A = πr², C = 2πr
- Triangle (Heron) A = √( s(s−a)(s−b)(s−c) ) s is half the perimeter.
- Trapezoid A = ½(a + b)h The average of the parallel sides, times the height.
- Regular polygon A = n s² ÷ (4 tan(π/n))
- Cylinder V = πr²h, S = 2πr(r + h)
- Sphere V = (4/3)πr³, S = 4πr²
- Cone V = ⅓πr²h, S = πr(r + l) l is the slant height, √(r² + h²).
- Cone frustum V = ⅓πh(R² + Rr + r²) A cone with the tip cut off.
- Spherical cap V = (πh²/3)(3R − h) A dome, or a partly filled spherical tank.
Which unit should I use?
Whichever your measurements are already in — just make sure all of them match. The unit selector only labels the answer and drives the conversion table; it does not convert your inputs for you, because there is no way to know which box you meant to change.
How do I work out an irregular room?
Split it into rectangles and triangles on paper, calculate each piece here, and add the results. For a room with one rectangular notch cut out of it, the L-shaped room entry does the subtraction for you.
Why is the surface area of my ellipsoid marked as approximate?
Because the exact value requires an elliptic integral, which has no closed form in ordinary functions. The figure shown uses Knud Thomsen's formula, which stays within about 1% for any realistic shape. The volume, by contrast, is exact.
How many litres will my cylindrical tank hold?
Pick the cylinder, enter the radius and height in metres, and read the capacity in litres figure. If your tank is only partly full, use the height of the liquid rather than the height of the tank.
What is the difference between the slant height and the height of a cone?
The height is straight up from the centre of the base to the tip. The slant height runs up the sloping surface from the edge of the base to the tip, and is always longer. Volume uses the vertical height; surface area uses the slant. The calculator works out the slant for you and shows it.