Cuboid – surface area and volume calculator
Enter three edges or move the sliders – the box changes shape and the area and volume are worked out instantly.
Three methods, one result
Method 1 · Face by face
Bottom and top: 2 · 5 · 3 = 30
Front and back: 2 · 5 · 2 = 20
Sides: 2 · 3 · 2 = 12
Pc = 30 + 20 + 12 = 62
Method 2 · Pairs of faces
One face from each pair: 15 + 10 + 6 = 31
Each face has a matching pair: 2 · 31 = 62
Method 3 · Wrap-around strip
The side faces unrolled into one rectangle: perimeter of the base × height.
Perimeter of the base: 2 · (5 + 3) = 16; strip: 16 · 2 = 32
Two bases: 2 · 15 = 30; Pc = 32 + 30 = 62
Volume – layers of cubes: 5 · 3 = 15 cubes 1 × 1 × 1 fit on the bottom, number of layers: 2. V = 15 · 2 = 30.
In litres (sizes in cm, 1 l = 1 dm³ = 1000 cm³): 30 cm³ = 0,03 l.
Watch out: surface area (how much paper covers the faces) is not volume (how much fits inside). 5 · 3 · 2 = 30 is the volume, not the area.
How do you find the surface area of a cuboid?
A cuboid (prostopadłościan) has six faces (ściany). Every face has a matching partner with the same area: bottom and top, front and back, left and right side. So the total surface area (pole powierzchni całkowitej, Pc) is Pc = 2 · (a · b + a · H + b · H).
For a 5 × 3 × 2 box the faces measure 15, 10 and 6, which add up to 31. Each one has a partner, so Pc = 2 · 31 = 62.
The wrap-around strip gives the same result: the four side faces unrolled into one rectangle are as long as the perimeter of the base (obwód podstawy), 2 · (5 + 3) = 16, and 2 high. The strip is 16 · 2 = 32, plus two bases of 15 each: 32 + 30 = 62. The strip works for every right prism (graniastosłup prosty), even when the base is a triangle.
Polish textbooks write total surface area as Pc, volume as V and height as H. The dot · means multiplication, and Poland uses a decimal comma: 2,5 means 2.5.
How do you find the volume of a cuboid?
Volume (objętość) is V = a · b · H: the area of the base times the height. On the bottom of a 5 × 3 × 2 box there is room for 5 · 3 = 15 unit cubes, and there are two such layers: V = 15 · 2 = 30.
How many litres does a cuboid hold?
1 litre is 1 dm³, which is 1000 cm³. A 50 × 30 × 20 cm aquarium holds 30 000 cm³, so 30 litres. It is quicker in decimetres: 5 · 3 · 2 = 30 dm³ = 30 l.
When do Polish schools teach the cuboid?
Pupils work out the volume and surface area of a cuboid in grades 4–6 (podstawa programowa, the national curriculum, Dz.U. 2024 poz. 996). Grades 7–8 add other right prisms and pyramids (ostrosłupy). The Polish eighth-grade exam (egzamin ósmoklasisty) also tests requirements from grades 4–6 – in 2025 question 15 was about the surface area of a cuboid.
What is the most common mistake?
Mixing up area and volume. Area tells you how much paper covers the faces (squares, cm²). Volume tells you how much fits inside (cubes, cm³). In the 2025 Polish eighth-grade exam, question 15 on the surface area of a cuboid was answered correctly by 52% of pupils, while about 27% chose the volume instead of the area (CKE report 2025, in Polish).
Glossary: English – Polish
- cuboid – prostopadłościan
- face – ściana
- edge – krawędź
- length, width, height – długość, szerokość, wysokość
- total surface area – pole powierzchni całkowitej (Pc)
- volume – objętość (V)
- perimeter of the base – obwód podstawy
- unit cube – kostka, sześcian
- right prism – graniastosłup prosty
The calculator works in your browser and sends nothing. Use at most two decimal places (2,5 and 2.5 both work). Spotted a mistake? Write to: kontakt@mamwynik.pl.