Rectangular prism calculator
Use this rectangular prism calculator with length, width and height – or with length, width and volume. For 4 × 3 × 12 the volume is 144, the surface area 192 and the space diagonal 13, with the calculation steps.
Example: Known values: Length, width and height · Length a 4 · Width b 3 · Height c 12 → Result: Volume V = 144 · Surface area S = 192. Source: Wikipedia – Quader. Updated: .
How it is calculated
A rectangular prism (cuboid) has six rectangular faces and is defined by length a, width b and height c. A cube is the special case a = b = c. If you know the volume instead of the height, the tool uses c = V ÷ (a · b).
The formulas
- Volume: V = a · b · c
- Surface area: S = 2 · (a·b + a·c + b·c)
- Lateral surface area: L = 2 · c · (a + b)
- Space diagonal: d = √(a² + b² + c²)
- Edge sum: 4 · (a + b + c)
How to use it
Enter the dimensions. Example: a = 4, b = 3 and c = 12 give V = 144, S = 2 · (12 + 48 + 36) = 192, L = 168 and d = √(16 + 9 + 144) = 13. The space diagonal is the longest straight line inside the box, such as the longest rod that fits in a carton. The unit is up to you; areas are in its square, the volume in its cube.
Frequently asked questions
How do you calculate the volume of a rectangular prism?
V = a · b · c, length times width times height. For 4 · 3 · 12 that is 144 cubic units.
How do you calculate its surface area?
S = 2 · (a·b + a·c + b·c): the sum of the six rectangles, which come in three equal pairs.
How do you calculate the space diagonal?
d = √(a² + b² + c²), the three-dimensional Pythagorean theorem. For 4, 3 and 12, d is exactly 13.
How do you find the height from the volume?
c = V ÷ (a · b). Choose “Length, width and volume” as the known values.
What is the difference between a cuboid and a cube?
A cube has three equal edges. Set a = b = c and you get V = a³ and S = 6 · a².
Sources and legal basis
As of: · Editorial policy
Related tools
- Volume CalculatorVolume calculator for 12 shapes: cylinder, box, sphere, cone, prism, horizontal tank … Mix cm, m, inches and feet – with litres, gallons, formula and sketch.
- Sphere calculatorSphere calculator: enter the radius, diameter, volume, surface area or circumference and get every measure of the sphere with formulas and steps. Free.
- Square Footage CalculatorSquare footage calculator for rooms and whole homes: enter feet and inches or metres, add rooms and L-shapes, get sq ft, m², sq yd, acres, waste and cost.
- Circumference CalculatorCircumference calculator that also gives perimeter and area of a circle, rectangle, square, ellipse, triangle, trapezoid, parallelogram or polygon.
- CBM calculatorCBM calculator for shipping: enter length, width and height in cm, mm, m, inches or feet plus the number of cartons and get cubic meters and cubic feet.
- Cylinder CalculatorCylinder calculator from any two values: radius, diameter, circumference, height, volume, lateral or surface area – with formulas, litres and working.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Glass Weight CalculatorGlass weight calculator: enter the width, height and thickness of a pane and get its weight in lb and kg – float glass, borosilicate, acrylic or custom.
- Cubic meters to cubic feet converterCubic meters to cubic feet: multiply by 35.3147, so 10 m³ = 353.1467 ft³. Convert m³ to ft³ or back, with cubic yards, liters and a conversion chart.