Volume Calculator: Formulas, Real-World Steps, & Units

Juggling unit conversions on a scratchpad—feet on the blueprint, meters on the spec sheet, gallons in the tank quote—is tedious and easy to get wrong. We built this page so you can pick a shape, enter real dimensions with the unit that matches your tape measure, and get a cubic result without redoing the arithmetic by hand.

How to Use This Volume Calculator

• Match your object to a block above. Spheres, drums, shipping boxes, culvert pipe, and pill-shaped tanks each have their own calculator—scroll until the label fits what you are measuring.
• Enter positive numbers only. Beside each label, choose the length unit you actually measured (m, cm, ft, in, and others). Mixed units on one shape are fine—the tool converts before it runs the formula.
• Press Calculate. Volume prints in cubic units tied to the first dimension on that block (meters → m³, feet → ft³, and so on).
• Spherical cap only: fill in any two of base radius r, ball radius R, and cap height h; leave the third field empty.

For dependable decimals on every shape, see why readable calculator output matters.

Volume Formulas and Practical Applications

Moving onto the math: each shape below shows how working crews and office estimators actually use these formulas. We varied the examples on purpose—storage tanks, packaging, site pours, and pipe runs—so you are not reading the same template eleven times.

Sphere volume

Whether you are quoting a round fuel storage vessel or checking how much water fits in a dome-end tank, picture a sphere as a uniform ball: one radius r from center to skin defines the whole solid.

V = (4/3)πr³

On a recent yard check, a half-meter radius round tank came out to about 0.524 m³—roughly 524 liters of capacity. Plug r = 0.5 m into the sphere block above to match that run.

Cone volume

Traffic cones, pour chutes, and hopper outlets all taper to a point. Use the vertical height h (straight up from base to tip), not the slanted side length—mixing those up is the most common cone mistake we see on site.

V = (1/3)πr²h

A lab beaker cone with r = 3 cm and h = 10 cm holds about 94.25 cm³—one-third of what a straight cylinder with the same base and height would hold.

Cube volume

A shipping cube or crate is the fastest volume on the list: measure one edge a and cube it.

V = a³

A 2 ft pallet cube offers 8 ft³ of usable space before voids around product.

Cylinder volume

Drums, silo sections, and concrete piers are right circular cylinders—flat circular ends joined by a straight wall. Base area times height does the job.

V = πr²h

In our testing, a 3 ft radius barrel 4 ft tall came out near 113.1 ft³—handy when ordering fill or checking spill containment.

Rectangular tank volume

Aquariums, IBC totes, and concrete troughs are boxes: length × width × height. Unlike a cube, the three edges can differ.

V = l × w × h

A stock crate at 4 ft × 3 ft × 2 ft gives 24 ft³—multiply the three numbers in any order; the product stays the same.

Capsule volume

Pill-shaped tanks and pressure vessels look like a cylinder wearing a hemisphere on each end. The tricky part: field h is only the straight cylindrical middle, not the overall length end-to-end.

V = πr²h + (4/3)πr³

A capsule with r = 1.5 ft and cylindrical section h = 3 ft totals about 35.3 ft³—useful when comparing round-ended tanks to plain cylinders.

Spherical cap volume

A spherical cap is what you get when a plane slices off the top of a ball—think of trimming a golf ball or capping a dome. Most people do not carry the three-way relationship between base radius, sphere radius, and cap height in their head; that is why this block accepts any two values and solves the third.

V = (1/3)πh²(3R − h)

With R = 1.68 in and h = 0.3 in, the removed cap volume is about 0.447 in³. When you know r and R instead, height follows h = R − √(R² − r²).

Conical frustum volume

Strip the tip off a cone and you have a frustum—the shape of a standard lampshade, a tapered bucket, or a takeout coffee cup sleeve. Label the smaller opening r and the larger base R.

V = (1/3)πh(r² + rR + R²)

A frustum with top 0.2 in, bottom 1.5 in, and height 4 in holds roughly 10.85 in³—handy for leftover fill in a tapered form.

Ellipsoid volume

An ellipsoid is a stretched ball—picture a rugby ball or an agricultural tank that is longer front-to-back than it is wide. You need three semi-axes because the shape is not uniform in every direction; that is why a diagram helps here.

V = (4/3)πabc

Semi-axes 1.5 in, 2 in, and 5 in give about 62.8 in³.

Square pyramid volume

Stockpiles, roof peaks, and monument bases often taper to a point over a square footprint. Height h is the vertical drop from base to apex—not the length of a sloped face.

V = (1/3)a²h

A 5 ft square base rising 12 ft to the peak encloses 100 ft³—the same one-third rule that applies to cones.

Tube (pipe) volume

Culvert pipe, conduit, and hollow shafting need wall material—or fluid in the annulus—not the solid core. Enter outer diameter d1, inner diameter d2, and run length l; outer must beat inner or the wall thickness is impossible.

V = π(d1² − d2²)l / 4

A 10 ft run with d1 = 3 ft and d2 = 2.5 ft needs about 21.6 ft³ of concrete in the wall—typical when sizing a creek crossing pipe.

When one object mixes shapes—a cylindrical silo plus a conical roof—run each piece separately and add the results. Same idea if you know mass and uniform density instead of sizes: volume equals mass divided by density, which is outside these geometry blocks.

Standard Units and Conversion Tables

Length units cube into volume units: measure in meters, report in cubic meters; measure in inches, report in cubic inches. The table lists each unit relative to one cubic meter and to milliliters (remember 1 mL = 1 cm³).

Frequently Asked Questions

What unit is the volume result in?

Volume prints in cubic units matching the first dimension’s length unit on that shape—m³ for meters, ft³ for feet, cm³ for centimeters. Different length units on one block are converted automatically before the formula runs.

How do you calculate the volume of a cylinder?

Multiply base area by height: V = πr²h, where r is the radius of the circular end and h is the perpendicular distance between the two flat faces. Try the cylinder section above or the cylinder block in the tool.

What is the difference between a capsule and a cylinder?

A cylinder has flat ends. A capsule adds a hemisphere on each end, so total length includes curved sections. Volume equals the straight wall πr²h plus both hemispheres (4/3)πr³—see the capsule notes for which segment counts as h.

How does the spherical cap calculator work?

Enter any two of base radius r, ball radius R, and cap height h. The tool computes the missing value, then applies V = (1/3)πh²(3R − h).

Why does the cone formula include a factor of one-third?

A cone with the same base and height as a cylinder fills exactly one-third of that cylinder. Pyramids and frustums follow the same taper logic, which is why 1/3 shows up again there.

Need flat triangle math instead of solids? Use the Pythagorean Theorem Calculator. For keypad expressions, open the Scientific Calculator. Browse the full math calculators hub for related tools.