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Volume Calculator | Compute Volume of Common 3D Shapes

Calculate the volume of boxes, cylinders, spheres, cones, pyramids and prisms, with conversions to gallons and litres included. Enter the dimensions and the tool applies the correct formula — perfect for tanks, aquariums, concrete and shipping estimates.

Last updated: July 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

ShapeFormula
Rectangular prisml × w × h
Cylinderπr²h
Sphere4/3πr³
Cone1/3πr²h

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

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Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

TipWhy
Use same unitsMixed units create wrong volumes
Cubic unitsVolume is always unit³
Round latePreserves accuracy

lightbulb Sizing a rectangular fish tank in gallons

An aquarium measures 48 in long, 18 in wide and 21 in tall. How many US gallons does it hold?

Result: About 78.5 US gallons. Volume = 48 × 18 × 21 = 18,144 cubic inches; divide by 231 (cubic inches per gallon) ≈ 78.5 gal.

What this means: Real stocking volume is lower once you subtract substrate, rocks and the gap below the rim — plan for roughly 90% of the calculated figure.

Formula & methodology

Formula: Volume depends on shape-specific dimensions

The Volume Calculator is built on a well-established calculation method. It uses the formula Volume depends on shape-specific dimensions to turn your inputs into a reliable result. Select a 3D shape — box, cylinder, sphere, cone, pyramid, or prism — enter its dimensions, and this calculator returns the volume in your choice of units (cubic meters, liters, gallons, cubic feet). Each result includes The steps are shown on the page so you can follow the reasoning from input to output.

Volume measures three-dimensional space. Choose the formula that matches the solid and keep all dimensions in the same unit before calculating.

What is the Volume Calculator?

The Volume Calculator is a free, browser-based math calculator tool that helps you Select a 3D shape — box, cylinder, sphere, cone, pyramid, or prism — enter its dimensions, and this calculator returns the volume in your choice of units (cubic. Instead of working through the math by hand or in a spreadsheet, you enter your values and the calculator returns an accurate result instantly — while still showing the formula and the steps so you can verify the reasoning. It is designed for quick everyday use: no sign-up, no installation, and everything runs locally in your browser for complete privacy.

How to use the Volume Calculator

  1. Enter the required values into the input fields.
  2. Press the calculate button — the result appears immediately, updated live as you change any value.
  3. Read the step-by-step breakdown below the result to see exactly how the calculation was performed.
  4. Use the interpretation guide to understand what the result means for your situation, and try different inputs to see how they change the outcome.

How to use the Volume Calculator

Select a 3D shape — box, cylinder, sphere, cone, pyramid, or prism — and enter its dimensions. The tool applies the shape-specific formula: length × width × height for a box, πr²h for a cylinder, 4⁄3πr³ for a sphere, and ⅓ × base area × height for cones and pyramids. Choose the unit system and the result is returned in cubic units, with a direct conversion to litres or US gallons where it is practical — the number you actually need for aquariums, pools, and tanks.

Interpreting your result

Volume is three-dimensional, so the units are always cubed. The practical conversion most people need is gallons: 1 cubic foot holds 7.48 US gallons, and 1 litre is 1,000 cm³, so a 48 × 18 × 21 inch aquarium is about 78.6 US gallons. For irregular containers, the tool can work from a measured liquid fill: enter the dimensions and the filled depth to get the partial volume. Understanding volume prevents both under-ordering (concrete, gravel) and over-filling (tanks, ponds).

Common mistakes to avoid

The most common error is mixing dimensions from different unit systems — an inch height with a metre length produces a wildly wrong volume. Second, using diameter where the formula needs radius: the cylinder and sphere formulas use r, and the volume changes by 2³ = 8× if you slip. Third, forgetting that volume scales with the cube: doubling a tank's dimensions multiplies its capacity by 8. Finally, ignoring wall thickness for practical capacity — a tank's stated outside size holds less than the geometric calculation because the walls and internal fittings take space.

Tips for best results

Measure inside dimensions for containers and outside dimensions for materials. Use the unit toggle to work in the system you measured with, and convert at the end. For pools and ponds, account for slopes and irregular bottoms by using the average depth rather than the deepest point. For cylinders like fuel tanks, measure the length and the internal diameter, not the overall length including fittings. When ordering concrete or gravel, add 5–10% for compaction and spillage, and check whether the supplier quotes cubic yards or cubic metres.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do I use the volume calculator?
Select a 3D shape — box, cylinder, sphere, cone, pyramid, or prism — and enter its dimensions in the fields shown. The tool applies the shape-specific volume formula and returns the result in your choice of cubic units, including gallons for practical uses like aquariums. For example, an aquarium measuring 48 × 18 × 21 inches holds about 78.6 US gallons.
What formula does the volume calculator use?
The Volume Calculator uses the standard Volume depends on shape-specific dimensions. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
Is the volume calculator accurate?
The Volume Calculator applies the standard formula: Volume depends on shape-specific dimensions. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.
Why do my results differ from another calculator?
The Volume Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Select a 3D shape — box, cylinder, sphere, cone, pyramid, or prism — enter its dimensions, and this calculator returns the volume in your choice of units (cubic meters, liters, gallons, cubic feet). Each result includes the formula used and a worked There is no limit on usage, and it works on any device.
How do I find the volume of a prism?
Any prism is base area × height, whatever the base shape. A triangular prism with a base of ½ × 6 × 4 = 12 cm² and a length of 10 cm holds 120 cm³. The same rule covers boxes (rectangle base) and cylinders (circle base) — find the base area first and the rest is one multiplication.
How do I get the radius of a sphere or cone from its volume?
Invert the formula. Sphere: r = (3V ÷ 4π)^(1/3), so a 500 cm³ ball has r = 4.92 cm. Cone: r = √(3V ÷ πh) — a 400 cm³ cone that's 12 cm tall has a base radius of √(1200 ÷ 37.7) = 5.64 cm. The calculator handles the cube- and square-root steps for you.
How do I convert measurements in feet into cubic feet?
Multiply the three dimensions while they're all in feet: a 4 ft × 3 ft × 2.5 ft box is 30 cubic feet. If a dimension is in inches, divide it by 12 first — mixing feet and inches in one multiplication is the single most common volume mistake. Divide cubic feet by 27 for cubic yards or multiply by 7.48 for US gallons.
What does the Volume Calculator do?
Select a 3D shape — box, cylinder, sphere, cone, pyramid, or prism — enter its dimensions, and this calculator returns the volume in your choice of units (cubic meters, liters, gallons, cubic feet). Each result includes the formula used and a worked. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
Is the Volume Calculator free and private?
Yes — the Volume Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Volume Calculator?
The volume formulas — such as l×w×h for a box and πr²h for a cylinder — are applied with full precision, so results are exact for the dimensions you enter. The gallon and litre conversions use the standard factors (7.48 gallons per cubic foot, 1,000 cm³ per litre). Practical accuracy depends on your measurements, particularly the average depth for irregular containers.

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