Disc Volume Calculator
How much material is actually in that round, flat part? Enter the radius or diameter plus the thickness and this disc volume calculator returns the volume instantly, for solid discs and for hollow discs with a center hole, in inches, centimeters, or millimeters. Add a material density and it converts the volume into an estimated weight as well, which is the number you need for ordering stock, checking a design, or costing a batch of parts.
Leave the density field blank to skip the weight estimate. Common densities: steel 7.85, aluminum 2.70, brass 8.50, plastic (ABS) 1.05, wood (oak) 0.75 g/cm³.
Quick Answer
Key takeaways
- A disc is a short cylinder: volume is π × radius² × thickness, and every measurement must share one unit before the math means anything.
- For a disc with a hole, subtract the squares of the radii, π × (R² − r²) × t. Squaring the difference of the radii instead is a published error on at least one ranking calculator, and it badly understates the material.
- Volume becomes weight with one multiplication by density. The optional density field does it for you and reports grams, kilograms, and pounds.
- Diameter or radius both work in the solid tab. Just tell the tool which one you measured, because entering a diameter as a radius quadruples the answer.
- Quick Answer
- How to use the disc volume calculator
- The disc volume formula, and why the hollow version trips people up
- Worked examples: a steel blank and a large washer
- From volume to weight: the density step
- Common solid disc sizes at a glance
- Disc, cylinder, or ring: which shape is yours?
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
How to use the disc volume calculator
Start by matching the tab to your part, then work through the fields in order. The whole job takes under a minute once the part is measured.
Pick the tab. Solid disc covers blanks, pucks, coins, and weight plates with no center hole. Hollow disc covers washers, rings, bushings, and brake rotors where the center is cut out.
Measure and choose one unit. Measure across the full width for a diameter, or from the center to the edge for a radius, then measure the thickness face to face. Pick inches, centimeters, or millimeters and use that unit for every number. Mixing units mid-calculation is the most common way this goes wrong.
Add a density only if you want weight. The density field is optional. Leave it blank for volume alone, or enter the material density in g/cm³ (steel 7.85, aluminum 2.70, brass 8.50) and the result adds an estimated weight in grams, kilograms, and pounds.
Calculate and check the steps. The result box shows the volume, the weight if you asked for it, and the arithmetic line behind the number, so you can confirm the tool used the radius and thickness you expected.
The disc volume formula, and why the hollow version trips people up
A disc is a cylinder whose height happens to be small, so it uses the cylinder volume formula, face area times thickness, the same slicing idea formalized in the LibreTexts Calculus treatment of volumes by slicing.
Hollow disc: V = π × (R² − r²) × t, where R is the outer radius and r is the inner (hole) radius. The hollow formula is the outer disc minus the missing center cylinder, the same subtraction the washer method formalizes in calculus courses.
The hollow version is where errors creep in. The subtraction has to happen after each radius is squared, because you are removing the hole's face area from the outer face area. Writing it as π × (R − r)² × t squares the width of the ring wall instead, which answers a different question: the area of a much smaller disc whose radius is the wall thickness. On the washer sized below, that wrong version returns half the true material volume, and on tighter rings the shortfall grows to four times or more.
Radius and diameter mix-ups cause the other classic error. Because the radius is squared, entering a diameter where a radius belongs does not double the answer, it quadruples it. If you are unsure which measurement your calipers just gave you, the relationships on the circle formula calculator page (radius, diameter, and circumference from any one of them) settle it in seconds.
Worked examples: a steel blank and a large washer
Both examples below are the pre-filled defaults in the calculator, and both were run through the tool's own code to confirm the numbers.
Solid disc. A steel blank has a radius of 5 inches and a thickness of 0.5 inches. Volume = π × 5² × 0.5 = π × 25 × 0.5 = 39.2699 in³, which the tool reports as 39.27 in³. With steel at 7.85 g/cm³, the weight estimate is 39.2699 × 16.387064 × 7.85 = 5051.6 g, shown by the tool as 5.052 kg (11.137 lb). The conversion factor in the middle is just the volume restated in cubic centimeters, because the density is per cubic centimeter.
Hollow disc. A washer has an outer diameter of 30 cm, an inner diameter of 10 cm, and a thickness of 2 cm. Halving the diameters gives an outer radius of 15 cm and an inner radius of 5 cm. Volume = π × (15² − 5²) × 2 = π × (225 − 25) × 2 = π × 400 = 1256.637 cm³, reported as 1256.64 cm³. Run the same part through the wrong (R − r)² formula and you get π × (15 − 5)² × 2 = 628.32 cm³, exactly half here, and the gap widens or narrows with the proportions. Either way, it is not the amount of steel you would be ordering.
One honest note about the hollow result: the tool's step line restates the arithmetic in inches (76.6847 in³ for this washer) because it converts internally, then converts the final answer back to your chosen unit. The headline number, 1256.64 cm³, is the one to use.
From volume to weight: the density step
Weight is the reason most people want the volume in the first place, and it takes one extra multiplication: weight = volume × density. The catch is unit discipline. Densities are almost always published in g/cm³, so the volume has to be in cubic centimeters before you multiply. The calculator handles that conversion internally whenever you fill in the density field, whichever unit you measured in.
| Material | Density (g/cm³) | Weight of the 39.27 in³ example disc |
|---|---|---|
| Steel | 7.85 | 5051.6 g (5.052 kg) |
| Aluminum | 2.70 | 1737.5 g (1.737 kg) |
| Brass | 8.50 | 5469.9 g (5.470 kg) |
| Plastic (ABS) | 1.05 | 675.7 g (0.676 kg) |
| Wood (oak) | 0.75 | 482.6 g (0.483 kg) |
Published density tables such as the Engineering ToolBox density of materials list are the right place to confirm a value for a specific alloy or grade, since real densities shift a little between alloys. If you do not know a material's density but you can weigh a sample and measure it, the density calculator works it out from mass and volume. And when the part is a longer cylinder rather than a flat disc, the cylinder mass calculator runs the same volume-times-density logic in one step.
Common solid disc sizes at a glance
Small discs turn up constantly in workshops, so here are the volumes for common diameters at a half inch thickness, each one computed with the solid formula above. Double the thickness and every volume doubles with it.
| Diameter | Radius | Thickness | Volume |
|---|---|---|---|
| 2 in | 1 in | 0.5 in | 1.57 in³ |
| 4 in | 2 in | 0.5 in | 6.28 in³ |
| 6 in | 3 in | 0.5 in | 14.14 in³ |
| 8 in | 4 in | 0.5 in | 25.13 in³ |
| 10 in | 5 in | 0.5 in | 39.27 in³ |
Notice the pattern: going from a 5 inch radius to a 10 inch diameter sounds like the same step, and it is, but doubling the diameter quadruples the volume because the radius is squared. That is why a modest-looking size increase can wreck a material estimate or a shipping weight.
Disc, cylinder, or ring: which shape is yours?
The math on this page assumes a flat part with parallel faces and, for the hollow tab, a centered round hole. Most real parts fit that model well. A barbell weight plate, a jar lid blank, a coin, a hockey puck, and a cut slice of round bar are all discs. A washer, a ring gear blank, a gasket, and a flange are hollow discs. Once the part gets long relative to its diameter, a soup can or a pipe, it behaves like the cylinders covered by the circle volume calculator, though the underlying formula is identical: the disc is simply a cylinder with a small height.
Two shapes fall outside the model. A disc with an off-center hole needs the hole positioned before any honest volume can be given, and a tapered or dished part (many brake rotors, some pulleys) is only approximated here. For a slight taper, averaging the thickness at the edge and the center gets you close enough for ordering stock, but not for a press fit calculation.
What competing calculators miss
The top results for this search split into three camps, and each leaves something out. The simplest tools, such as BraveCalculator's version, take a diameter and a thickness in inches and stop there: no hollow mode at all, so every washer or ring has to be faked by hand, and no unit choice. CalculatorsHub covers both solid and hollow discs with the correct formulas, which is genuinely good, but it still ends at volume, with no way to turn the answer into the weight you actually need for ordering or shipping.
The third camp is worse than incomplete. CalculatorUltra publishes a hollow-disc formula of π × (R − r)² × t, squaring the difference of the radii instead of subtracting their squares. Its own worked example, outer radius 5, inner radius 3, thickness 0.5, returns 6.283 in³ under that formula; the correct annulus math gives π × (25 − 9) × 0.5 = 25.13 in³, four times as much material. Anyone who ordered stock from the smaller number would run out mid-job.
This calculator covers both shapes with the verified formulas, takes radius or diameter in the solid tab, works in inches, centimeters, or millimeters, shows the arithmetic behind every result, and adds the density-to-weight step the others skip. Unit conversions follow the exact definitions in the NIST guide to SI units for length, where 1 inch is exactly 25.4 mm.
Frequently Asked Questions
Either one. In the solid disc tab, use the "I measured the" selector to tell the tool which measurement you took. Across the widest point is the diameter, and the tool halves it. From the center to the edge is the radius, and it is used as entered.
Subtract the missing center from the full disc: volume = π × (outer radius² − inner radius²) × thickness. Watch out for tools that square the difference of the radii, π × (R − r)² × t. That is a different calculation, and it understates the material in a typical washer by a wide margin.
Multiply the volume by the material density. Enter a density in g/cm³ in the optional field and the tool reports the estimated weight in grams, kilograms, and pounds. Steel is 7.85 g/cm³, aluminum is 2.70 g/cm³, and brass is 8.50 g/cm³.
Yes. That is what the hollow disc tab is for: enter the outer diameter, the hole diameter, and the thickness. For a ventilated brake rotor the answer is an approximation, because the cooling vanes are air gaps, not solid material.
The tool models a perfect cylinder with flat, parallel faces. A small chamfer changes the true volume slightly. For precision work, measure the thickness at several points and enter the average, or work out the chamfer volume separately and subtract it.
The formula only works when every measurement shares one unit. Mixing inches for the diameter with millimeters for the thickness is the most common way to get a wildly wrong answer. Pick one unit in the selector and measure everything in it.
Yes. Enter 0 as the inner diameter and the hollow formula returns the solid disc volume, because the missing center has zero size. The solid tab is simpler for that job, but both routes give the same number.
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References
- LibreTexts, Calculus (OpenStax), Section 6.2, "Determining Volumes by Slicing" - the disk and washer methods, with the washer formula V = ∫ π[(f(x))² − (g(x))²] dx that the hollow disc calculation applies. LibreTexts: Determining Volumes by Slicing. Accessed October 2026.
- OpenStax, Calculus Volume 1, Section 6.2, "Determining Volumes by Slicing" - the disk and washer methods, including the π(R² − r²) subtraction used for hollow discs. OpenStax: Determining Volumes by Slicing. Accessed October 2026.
- Khan Academy, "Cylinder volume and surface area" - a worked walkthrough of the cylinder volume formula with practice examples. Khan Academy: Cylinder Volume and Surface Area. Accessed October 2026.
- National Institute of Standards and Technology, "SI Units: Length" - the exact definitions behind the unit conversions, including 1 inch = 25.4 mm exactly. NIST: SI Units, Length. Accessed October 2026.
- The Engineering ToolBox, "Density of Selected Solids" - published densities for steel, aluminum, brass, plastics, and woods used for the weight estimates. Engineering ToolBox: Density of Selected Solids. Accessed October 2026.