How Our Calculators Work
Last updated: October 16, 2026
This page explains how every calculator on CY Calculator turns your measurements into an answer: the formulas, the unit definitions, how numbers are rounded, which values are assumed until you change them, and how the results are checked. If a result ever looks wrong, the last section explains how to report it.
The Formulas
Every volume calculator follows the same two steps. First it finds the area of the shape you picked, then it multiplies that area by the depth. With everything in feet, that gives cubic feet, and dividing by 27 gives cubic yards, because a cubic yard is a cube 3 feet on each side. This is the method behind the main cubic yard calculator and every material calculator on the site.
| Shape | Area formula |
|---|---|
| Rectangle | length × width |
| Square | side × side |
| Circle | π × (diameter ÷ 2)² |
| Triangle | ½ × base × height |
| Trapezoid | ½ × (base 1 + base 2) × height |
| Rectangle border | (length + 2 × border) × (width + 2 × border) − length × width |
| Circle border | π × ((diameter ÷ 2 + border)² − (diameter ÷ 2)²) |
| Annulus (ring) | π ÷ 4 × (outer diameter² − inner diameter²) |
| Known area | the area you enter |
Volume = area × depth, and cubic yards = cubic feet ÷ 27. The weight calculators then multiply cubic yards by a density in tons per cubic yard, and the bag counts divide cubic feet by the volume of one bag. The square feet calculator stops at the area unless you add a depth.
Unit Definitions
Each length is converted to feet before anything is multiplied, using the definitions in the NIST Guide to the SI, Appendix B. The calculators use full values, not rounded ones such as 3.28 feet per meter.
| Unit | Definition |
|---|---|
| 1 foot | 12 inches = 0.3048 meter (exact) |
| 1 yard | 3 feet = 0.9144 meter (exact) |
| 1 inch | 25.4 millimeters (exact) |
| 1 cubic yard | 27 cubic feet ≈ 0.7646 cubic meter |
| 1 acre | 43,560 square feet |
| 1 US ton | 2,000 pounds ≈ 0.9072 metric tonne |
Rounding
- Every calculation runs at full precision. Only the numbers you see are rounded.
- Volumes, areas and weights are shown to two decimal places. Values smaller than 0.01 are shown to two significant figures so they do not appear as zero.
- The breakdown line under each result shows its working to four decimal places, so you can check it by hand.
- Bag counts always round up to a whole bag, because stores do not sell part of one.
- Costs are shown to the cent. When you price by the bag, the cost uses the whole number of bags.
Default Values
Some fields start with a typical value so you get an answer straight away. Change any of them to match your own job.
- Waste allowance: starts at 0%. The calculators never add extra on your behalf.
- Density: gravel and sand start at 1.4 tons per cubic yard and topsoil at 1.1. These are common starting points, not measurements of your material. Weight changes with the type of stone or soil and how wet it is, so use the figure your supplier quotes whenever you have one.
- Concrete bags: 40, 60 and 80 lb bags are counted at 0.30, 0.45 and 0.60 cubic feet, the yields listed on the QUIKRETE Concrete Mix data sheet. Other mixes can differ, so check your own bag.
- Mulch bags: you choose the size printed on the bag, from 1 to 3 cubic feet.
How We Test the Calculators
The worked examples and tables on every page are produced by the same code that runs the calculators, so the two cannot disagree. Before any update is published, more than 150 automated checks run, and the update stops if one fails. They cover:
- the area formula for every shape listed above;
- conversions between inches, feet, yards, millimeters, centimeters and meters, including mixed units in one calculation;
- known answers, such as 27 cubic feet making exactly one cubic yard, and 3 m × 2 m × 10 cm making 0.6 cubic meters;
- whole bag counts, waste allowances, quantities and costs per yard, bag and ton;
- typing mistakes such as empty fields, zero, negative numbers, letters and very large values, which must show a clear message instead of a broken result.
A separate check recalculates every sum written into our guides, so a wrong figure in an article stops the update too. When a calculator page changes, the date under the calculator changes with it.
What the Results Can and Cannot Tell You
A result is the volume of the shape you described. Real jobs differ from that shape: ground slopes, soil settles, gravel compacts, edges wander and some material is lost to spillage. Treat every result as an estimate, add your own allowance where it makes sense, and confirm quantities with your supplier or contractor before you order. Our Terms & Disclaimer cover the details.
Report a Result That Looks Wrong
If a calculator gives an answer you do not expect, please contact us with the calculator name, the shape, the numbers and units you entered, and the result you expected. We check every report, fix confirmed errors and update the page. The team behind the calculators reads every message.