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How This Calculator Works
Volume is the amount of three-dimensional space a solid takes up, and each common shape has its
own formula for finding it from a few basic measurements. Pick a shape — rectangular prism,
cube, sphere, cylinder, or cone — enter its dimensions, and this calculator returns both the
volume and the total surface area.
These five shapes are the solid, one-dimension-up counterparts of the Area Calculator’s own flat
shapes: a cube is a square with depth, a sphere is a circle with depth, a cylinder is a circle
extruded along a straight axis, and a cone tapers that same circle to a point.
A cone’s volume is exactly one-third of a cylinder with the same radius and height — the same
relationship a cone-shaped and cylinder-shaped container of equal base and height always have,
regardless of size.
Worked Example
A cylinder with a 5 m radius and 10 m height:
Square the radius: 52=25.
Multiply by π: 25×π≈78.54.
Multiply by the height: 78.54×10≈785.40 m3.
Its surface area — the two circular ends plus the curved side — works out to about 471.24 m²,
using 2×π×radius×(radius+height).
Cómo funciona esta calculadora
El volumen es la cantidad de espacio tridimensional que ocupa un sólido, y cada figura común
tiene su propia fórmula para calcularlo a partir de unas pocas medidas básicas. Elige una figura
— prisma rectangular, cubo, esfera, cilindro o cono —, ingresa sus dimensiones, y esta calculadora
devuelve tanto el volumen como el área de superficie total.
Estas cinco figuras son las contrapartes sólidas, un nivel dimensional más arriba, de las propias
figuras planas de la Calculadora de Área: un cubo es un cuadrado con profundidad, una esfera es un
círculo con profundidad, un cilindro es un círculo extruido a lo largo de un eje recto, y un cono
va estrechando ese mismo círculo hasta un punto.
El volumen de un cono es exactamente un tercio del de un cilindro con el mismo radio y la misma
altura — la misma relación que siempre tienen un recipiente en forma de cono y uno en forma de
cilindro con base y altura iguales, sin importar el tamaño.
Ejemplo resuelto
Un cilindro con un radio de 5 m y una altura de 10 m:
Eleva el radio al cuadrado: 52=25.
Multiplica por π: 25×π≈78.54.
Multiplica por la altura: 78.54×10≈785.40 m3.
Su área de superficie — los dos extremos circulares más el lado curvo — resulta en aproximadamente
471.24 m², usando 2×π×radio×(radio+altura).
What's the difference between this and the Area Calculator?
Area measures the two-dimensional space a flat shape covers; volume measures the three-dimensional space a solid takes up. This calculator's five shapes are the solid, one-dimension-up counterparts of most of the Area Calculator's own shapes — a cube instead of a square, a sphere instead of a circle, and so on.
How is a cone's surface area calculated?
It's the base circle's area plus the lateral (side) surface, which depends on the cone's slant height — the straight-line distance from the rim to the tip, found from the radius and height with the Pythagorean theorem (slant height = √(radius² + height²)), not the vertical height alone.
Can I switch units after entering my numbers?
Yes — changing the unit dropdown converts whatever you've already typed into the new unit rather than reinterpreting the same number, so your shape stays the same real-world size.
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