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Pick a solid, enter its measurements, and Axiom shows the formula and working.
V = l × w × h · SA = 2(lw + lh + wh)
Choose a box, cylinder, cone, or sphere and enter its positive dimensions in the same length unit. Press Calculate to see volume and total surface area; for a cone, enter vertical height rather than slant height.
Volume measures enclosed space in cubic units, while surface area measures the outside in square units. A box has V = lwh and SA = 2(lw + lh + wh); a cylinder has V = πr²h and SA = 2πr² + 2πrh. A right circular cone has V = πr²h/3 and SA = πr² + πr√(r² + h²). A sphere has V = 4πr³/3 and SA = 4πr².
Choose Box and enter length 2, width 3, height 4 cm. Volume = 2 × 3 × 4 = 24 cm³. Surface area = 2(6 + 8 + 12) = 52 cm².
Choose Cylinder with radius 3 cm and height 5 cm. Volume = 45π cm³, approximately 141.3716694 cm³. Total surface area = 18π + 30π = 48π cm², approximately 150.7964474 cm².
Choose Cone with radius 3 cm and vertical height 4 cm. Slant height = √(9 + 16) = 5 cm; volume = 12π ≈ 37.69911184 cm³; total surface area = 24π ≈ 75.39822369 cm².
Yes. This is total surface area: six box faces, both cylinder ends, and the cone’s circular base plus curved surface. It is not an open-container or lateral-area calculator.
Enter radius. Divide a diameter by 2 first; using the full diameter as radius makes both area and volume too large.
Vertical height runs perpendicular to the base. Slant height follows the cone’s side; the calculator derives it from radius and vertical height using the Pythagorean theorem.
Not directly. These formulas assume standard boxes, right circular cylinders/cones, and spheres. Convert units first and split composite solids yourself; use ordinary-sized dimensions because extreme values can exceed the numeric range.
The Unit Converter helps prepare consistent measurements, while the Pythagorean tool supports finding a cone’s slant height. Read the surface area and volume lesson to decide which measure a problem needs. Related tools: Unit Converter, Pythagorean Theorem Calculator. Read the Surface Area & Volume lesson or practice surface area & volume to build confidence without relying on a calculator.