Volume Calculator (Box, Cylinder, Cone, Sphere, Pyramid)
Pick a 3D shape—box, cylinder, cone, sphere, or square pyramid—enter dimensions, and instantly get volume and surface area with clear formula steps.
Your 3D shape
Results
Steps
- Volume V = L × W × H = 10 × 6 × 4 = 240
- Surface area A = 2(LW + LH + WH) = 2(60 + 40 + 24) = 248
Results interpretation
- Volume vs. area: volume scales with the third power of size; surface area scales with the second.
- Doubling a dimension can multiply volume by 2×, 4×, or 8× depending on shape and which side doubles.
- Who it’s for: students, DIYers, contractors, makers—any task involving filling, pouring, or coating.
How to use the volume calculator
- Select a shape and unit.
- Enter positive dimensions in the same unit.
- Read volume (cm³) and surface area (cm²), plus the formula steps.
- Adjust dimensions to explore “what if” scenarios.
How this calculator works
Formulas & assumptions
- Box: V = L·W·H; A = 2(LW + LH + WH).
- Cylinder: V = πr²h; A = 2πr(r + h) (top + bottom + side).
- Cone: V = (1/3)πr²h; A = πr(r + s) with s = √(r² + h²).
- Sphere: V = (4/3)πr³; A = 4πr².
- Square pyramid (right): V = (1/3)b²h; A = b² + 2bs where s = √((b/2)² + h²).
Assumptions: perfect solids, consistent units, and total surface area (including bases).
Use cases & examples
Example 1 (box planter): 40 × 25 × 30 cm → V = 30,000 cm³. Liner needed ≈ surface area 2(LW + LH + WH) = 5,900 cm².
Example 2 (cylinder tank): r = 60 cm, h = 120 cm → V ≈ 1,357,168.0264 cm³.
Example 3 (cone pile): r = 3 cm, h = 5 cm → V ≈ 47.1239 cm³; s = √(3²+5²) ≈ 5.831 cm.
Volume Calculator: Fast 3D Shape Volume and Surface Area
Our volume calculator converts simple measurements into the total space a 3D object occupies. Whether you’re estimating concrete, soil, water, grain, or packaging capacity, knowing volume—and surface area for coatings—prevents costly over- or under-ordering. This tool covers the most common solids: box (rectangular prism), cylinder, cone, sphere, and square pyramid. Enter dimensions once in your preferred units and the calculator shows both volume in cm³ and surface area in cm²along with transparent formula steps so you can double-check the math.
The key to accuracy is unit consistency. If dimensions are in inches, results return cubic inches and square inches; for meters, you’ll see cubic meters and square meters. Many practical jobs simply need a quick sense of scale: doubling a cylinder’s radius quadruples its area but increases volume eightfold. That’s why slight size changes can have big cost impacts for fill materials and coatings.
Boxes and cylinders dominate storage and shipping, while cones and pyramids appear in hoppers, piles, and architectural features. Spheres show up in tanks, bearings, and sports. The formulas here are standard: V = L·W·H for boxes; V = πr²h for cylinders; V = (1/3)πr²h for cones; V = (4/3)πr³ for spheres; and for a right square pyramid V = (1/3)b²h. Surface areas differ by shape. For example, a cylinder’s A = 2πr(r + h) includes both circular ends plus the curved side, while a cone’s A = πr(r + s) depends on slant height s.
For DIY and construction, round up fill materials to account for settling and spillage, and add a margin to coatings for waste and texture. In coursework, show your steps and units; this calculator’s “Steps” box is designed to mirror the reasoning teachers expect. Use the related tools to convert areas, work with circles and triangles, or run quick checks on percentages and basic arithmetic.
By combining shape pickers, instant feedback, and clear assumptions, this volume calculator speeds planning without sacrificing clarity. Enter dimensions, verify the units, and you’ll have trustworthy numbers for both capacity and coverage.
Volume Calculator — FAQ
Do I need to convert units first?
No—just keep all dimensions in the same unit. Results use the matching squared/cubed unit.
Does cylinder area include the top and bottom?
Yes. This calculator reports total surface area by default (both ends plus curved side).
What’s slant height on a cone or pyramid?
It’s the length from the tip to the edge along the face. It appears in total surface area formulas.
Can I use feet and inches together?
Enter either all inches or all feet. Mixed units require converting first for correct results.
Which shapes are supported?
Box (rectangular prism), cylinder, cone, sphere, and right square pyramid.