How Do You Measure the Volume of a Solid? A Complete Guide

To measure the volume of a solid, you either apply a geometric formula (for regular shapes like cubes, spheres, and cylinders) or use water displacement (for irregular shapes that have no simple formula). Both approaches express volume in cubic units—such as cubic centimeters (cm³) or milliliters (mL), which are equivalent. The method you choose depends on whether the object has a predictable, measurable shape.

Regular Solids: Formula Methods

A regular solid is an object with a defined geometric shape—a cube, rectangular prism, sphere, cylinder, cone, or pyramid. Because the shape is predictable, you can calculate its volume from a few linear measurements rather than submerging it in liquid. Volume is a three-dimensional measurement, so these formulas multiply three length dimensions (or the equivalent for curved shapes).

Here are the standard formulas, with each variable defined:

• Cube: V = s³, where s is the length of one edge.
• Rectangular prism (box): V = l × w × h (length × width × height).
• Sphere: V = (4/3)πr³, where r is the radius (half the diameter).
• Cylinder: V = πr²h, where r is the radius of the circular base and h is the height.
• Cone: V = (1/3)πr²h.
• Pyramid: V = (1/3) × base area × height.

The key is matching your measurements to the shape’s requirements. A cube needs only one measurement; a sphere needs the radius; a cylinder needs radius and height. If you measure the diameter instead of the radius, divide by two before plugging in. These relationships are standard geometry covered in most curricula, such as Khan Academy.

Units matter. If you measure in centimeters, your answer is in cubic centimeters. If you measure in inches, the result is cubic inches. Keep all dimensions in the same unit before calculating—mixing centimeters and meters will produce a wrong answer.

Not every object is a clean geometric shape. A rock, a key, or a piece of jewelry has no simple formula. For these, you switch to the displacement method.

Irregular Solids: Water Displacement

An irregular solid is any object without a defined geometric shape, so formulas don’t apply. The displacement method works on a principle attributed to Archimedes: an object submerged in liquid pushes aside (displaces) a volume of liquid exactly equal to the object’s own volume.

Here’s the procedure using a graduated cylinder:

1. Fill the cylinder with water to a comfortable level and record the starting volume (for example, 50 mL).
2. Tilt the cylinder and gently slide the object in, or lower it with a string, to avoid splashing.
3. Record the new water level (for example, 72 mL).
4. Subtract the starting volume from the final volume: 72 mL − 50 mL = 22 mL. The object’s volume is 22 cm³.

Because 1 mL equals 1 cm³, the reading converts directly to cubic centimeters. If the object floats, push it under with a thin rod or pin so it is fully submerged—but don’t let the rod enter the water any deeper than necessary, or you’ll add extra displacement.

For objects too large for a graduated cylinder, use an overflow can (also called a Eureka can). Fill it to the spout, let the excess drain, then lower the object in. The water that spills out equals the object’s volume. Catch the overflow in a graduated cylinder. One caution: porous materials like wood or sponge absorb water, which throws off the reading. Seal them with a thin coat of wax or use a different method if accuracy matters.

Measuring Tools and Accuracy

Choosing the right tool determines how precise your volume calculation will be. The National Institute of Standards and Technology emphasizes that measurement accuracy depends on both the instrument and the technique—every tool has a limit, and reading it correctly matters as much as owning it.

Linear measuring tools (for regular solids):

• Ruler or meter stick: Good for boxes and cubes; read to the nearest millimeter.
• Calipers: Measure internal, external, and depth dimensions with precision—often to 0.01 mm (0.001 cm). Best for small regular solids like metal cylinders where a ruler would introduce error.
• Micrometer: Even finer, typically to 0.01 mm, for tiny precision parts.

Volume tools (for irregular solids):

• Graduated cylinder: The workhorse for displacement. Choose one sized close to your expected volume—a 100 mL cylinder reads more precisely than a 1000 mL one for small objects.
• Burette: For very small volumes, with fine graduations.
• Overflow can: For large or awkward objects.

Mass tools (supporting role):

• Balance or scale: Measures mass, not volume, but useful when you know density. Since density = mass ÷ volume, you can calculate volume as mass ÷ density—handy for regular metal objects of known material.

To read accurately, view the meniscus (the curved water surface) at eye level; looking from an angle skews the reading. Take at least three readings and average them to reduce random error. And keep unit conversions straight: 1 mL = 1 cm³; 1 L = 1000 cm³; 1 m³ = 1,000,000 cm³. Writing units at every step keeps them from getting tangled.

A Worked Example

Start with a rectangular block: length 8.0 cm, width 5.0 cm, height 3.0 cm.

V = l × w × h = 8.0 × 5.0 × 3.0 = 120 cm³

Now confirm with displacement. Fill a graduated cylinder to 50.0 mL, submerge the block, and read 170.0 mL. The difference is 120.0 cm³—the same answer, which is a good sign both your formula and your technique are sound.

Key Takeaways

• Volume of a regular solid comes from a geometric formula: cube (s³), box (l×w×h), sphere ((4/3)πr³), cylinder (πr²h), cone ((1/3)πr²h).
• Volume of an irregular solid comes from water displacement: final water level minus starting level equals the object’s volume in mL, which equals cm³.
• Read instruments at eye level and average multiple trials to reduce error; use calipers for small regular solids and a graduated cylinder or overflow can for irregular ones.
• Keep units consistent and convert correctly—1 mL = 1 cm³, 1 m³ = 1,000,000 cm³—so the answer stays accurate.
• Use the density relationship (volume = mass ÷ density) as a cross-check when the material is known.