3 calculators
Geometry Calculators
These geometry calculators handle common shape math for surfaces, rooms, containers, fill levels, and simple 3D objects. Choose the shape, enter the dimensions, and use the worked formulas to verify the result.
Tools in this category
Which calculator answers which question
| What you are asking | Use | Answers in |
|---|---|---|
| How much surface is there to cover? | Area calculator | m², ft², acres, hectares |
| How much will this container hold? | Volume calculator | litres, gallons, m³, ft³ |
| How much material do I need to buy? | Material calculator | bags, packs, tonnes |
| What will it weigh once filled? | Volume calculator | kg, from volume and density |
Area formulas
| Shape | Formula | You measure |
|---|---|---|
| Rectangle | A = length × width | two sides |
| Square | A = side² | one side |
| Triangle | A = ½ × base × height | base and perpendicular height |
| Parallelogram | A = base × height | base and perpendicular height |
| Trapezoid | A = ½ × (a + b) × height | both parallel sides and the gap |
| Circle | A = π × radius² | radius, or diameter ÷ 2 |
| Ellipse | A = π × a × b | both semi-axes |
The height in a triangle or trapezoid is the perpendicular height, not the length of a sloping side. Using the slope instead is the most common source of an area that comes out too large.
Volume formulas
| Solid | Formula |
|---|---|
| Box | V = length × width × height |
| Cube | V = side³ |
| Cylinder | V = π × radius² × height |
| Sphere | V = 4/3 × π × radius³ |
| Cone | V = π × radius² × height ÷ 3 |
A cone is exactly one third of the cylinder that encloses it, and a sphere is exactly two thirds of it — worth remembering as a check on any result that looks wrong.
Land and floor area units
| Unit | In square metres | Also equals |
|---|---|---|
| 1 square foot | 0.0929 m² | 144 square inches |
| 1 square yard | 0.8361 m² | 9 square feet |
| 1 square metre | 1 m² | 10.764 square feet |
| 1 are | 100 m² | a 10 × 10 m square |
| 1 acre | 4,046.86 m² | 43,560 square feet |
| 1 hectare | 10,000 m² | 2.471 acres |
| 1 square mile | 2,589,988 m² | 640 acres |
Doubling a dimension does not double the result
This catches people out on every quoting job. Area scales with the square of length and volume with the cube:
| If every dimension is… | Area becomes | Volume becomes |
|---|---|---|
| × 1.5 | × 2.25 | × 3.4 |
| × 2 | × 4 | × 8 |
| × 3 | × 9 | × 27 |
A pizza of twice the diameter is four pizzas, not two. A tank built 25% larger in every direction holds nearly double. And a 10% measuring error on each side of a room compounds to a 21% error in the flooring order.
From area to a materials order
The geometric answer is the starting point, not the quantity to buy. Real orders add coverage rate and waste:
Packs needed = area ÷ coverage per pack × (1 + waste allowance)
| Job | Typical waste allowance | Why |
|---|---|---|
| Straight-laid tile or laminate | 10% | cuts at walls, breakages |
| Diagonal or herringbone laying | 15–20% | every edge piece is an angled cut |
| Patterned wallpaper | 15% | pattern repeat must align between drops |
| Paint | second coat | coverage figures assume one coat on primed surface |
| Concrete, screed, gravel | 5–10% | uneven substrate and compaction |
Buy tiles from a single batch while you are at it — dye lots differ visibly, and a later top-up rarely matches. The material calculator applies coverage and waste to an area for you.
Volume to weight
Capacity and load are different questions, and floors, shelves and vehicles fail on the second one. Multiply volume by density to get weight — water is the easy case at 1 kg per litre, but most things are not water:
| Material | Density | 1 m³ weighs |
|---|---|---|
| Petrol | 0.74 kg/L | 740 kg |
| Fresh water | 1.00 kg/L | 1,000 kg |
| Dry sand | 1.6 kg/L | 1,600 kg |
| Gravel | 1.7 kg/L | 1,700 kg |
| Concrete | 2.4 kg/L | 2,400 kg |
A modest 1.2 × 0.8 × 0.6 m aquarium holds 576 litres and therefore puts well over half a tonne on the floor once filled. The volume calculator estimates filled weight directly from the fill level and density you enter.
Worked examples
Flooring for an L-shaped room
There is no formula for an L. Split it into two rectangles, calculate each, and add. A room that is 4 × 3 m with a 2 × 1.5 m alcove is 12 + 3 = 15 m². At 10% waste that is 16.5 m² to order — and since laminate sells in packs of around 2.2 m², eight packs.
Turf for a circular lawn
Measure across the widest point and halve it: a 7 m diameter gives a 3.5 m radius, so π × 3.5² = 38.5 m². Measuring the diameter and using it as the radius is the classic error here, and it overstates the order by a factor of four.
Water in a cylindrical tank at part fill
A tank 0.6 m in radius and 1.8 m tall holds π × 0.36 × 1.8 = 2.04 m³, or 2,036 litres. Filled to 70% that is 1,425 litres, weighing about 1,425 kg — which is the figure that matters for the stand it sits on.
Paint for four walls
Perimeter × height gives the wall area: a 5 × 4 m room with 2.5 m ceilings is 18 × 2.5 = 45 m². Subtract roughly 1.8 m² per door and 1.5 m² per window, so with one of each, 41.7 m². Paint covering 12 m² per litre needs 3.5 litres per coat — 7 litres for two.
The formulas behind this category, and the published sources they come from, are listed on the methodology page.
Other categories
Geometry — common questions
Which shapes are supported?
The area calculator covers common flat shapes such as rectangles, triangles, circles, and trapezoids. The volume calculator covers common solids such as boxes, cylinders, cones, and spheres.
Can I use different measurement units?
Yes. You can calculate with the units you have, then use the unit converter, length converter, or volume converter when you need to switch between metric and imperial units.