Square Feet to Square Yards Calculator
Convert square feet to square yards: 1 sq yd = 9 sq ft, exactly, because a yard is 3 feet. Type either box — it runs both ways.
Last updated:Conversion Formula
Conversion factors follow NIST Special Publication 811, Appendix B.9.1 (area). Links are in Sources below.
square yards = square feet ÷ 9
square feet = square yards × 9 (1 sq ft = 1/9 sq yd = 0.111111… sq yd — the 1 repeats forever)
Divide by 9 rather than multiplying by a truncated 0.1111111111111111: the division is exact in every case, the decimal never is. Other units one square yard equals exactly: 9 sq ft, 1,296 sq in, 0.83612736 m², 1/4,840 acre.
Worked Example
A bedroom measures 12 ft × 15 ft and the carpet is quoted per square yard. You want 10% waste for matching and offcuts.
- Area in sq ft: 12 × 15 = 180 sq ft.
- Convert: 180 ÷ 9 = 20 sq yd.
- Add waste to the area: 180 × 1.10 = 198 sq ft, and 198 ÷ 9 = 22 sq yd to order.
- Check the other way: 22 × 9 = 198 sq ft. ✓
Order of operations matters. Rounding 20 sq yd up to a whole roll increment and then adding 10% is not the same as adding 10% to 180 sq ft and then dividing. Convert first, add waste to the area, round last — and round the linear cut length, because carpet comes off a roll in whole feet, not in whole square yards.
Carpet waste table
Waste is added to the area (× 1.10 for 10%), then converted. The last column rounds the sq yd up to a whole yard, which is how orders are placed.
| Room size | Sq ft | Sq yd | Sq yd + 10% waste |
|---|---|---|---|
| 10 × 10 | 100 | 11.11 | 12.22 → 13 sq yd |
| 12 × 12 | 144 | 16.00 | 17.60 → 18 sq yd |
| 12 × 15 | 180 | 20.00 | 22.00 → 22 sq yd |
| 15 × 20 | 300 | 33.33 | 36.67 → 37 sq yd |
| 20 × 20 | 400 | 44.44 | 48.89 → 49 sq yd |
If the roll is 12 ft wide, each linear foot you buy is 12 sq ft = 1.3333 sq yd. A 12 ft × 15 ft room therefore needs 15 linear feet off a 12 ft roll with no seam, and 15 × 12 = 180 sq ft exactly. Use the carpet calculator to add padding and price.
Quick Reference
| Square Feet | Square Yards |
|---|---|
| 1 sq ft | 0.1111 sq yd |
| 4.5 sq ft | 0.5 sq yd |
| 9 sq ft | 1 sq yd |
| 18 sq ft | 2 sq yd |
| 27 sq ft | 3 sq yd |
| 45 sq ft | 5 sq yd |
| 90 sq ft | 10 sq yd |
| 100 sq ft | 11.1111 sq yd |
| 144 sq ft | 16 sq yd |
| 180 sq ft | 20 sq yd |
| 225 sq ft | 25 sq yd |
| 300 sq ft | 33.3333 sq yd |
| 450 sq ft | 50 sq yd |
| 900 sq ft | 100 sq yd |
| 1,500 sq ft | 166.6667 sq yd |
| 2,000 sq ft | 222.2222 sq yd |
| 43,560 sq ft (1 acre) | 4,840 sq yd |
| 27,878,400 sq ft (1 sq mi) | 3,097,600 sq yd |
What is a square yard?
A square yard is the area of a square one yard on each side. The yard is exact by international agreement: 1 yd = 3 ft = 36 in = 0.9144 m, the last figure following from 1 ft = 0.3048 m exactly. So a square yard is 3 ft × 3 ft = 9 sq ft, or 36 in × 36 in = 1,296 sq in, or 0.9144 m × 0.9144 m = 0.83612736 m².
NIST SP 811 prints the square-yard factor as 8.361 274 E−01 m². That is 0.83612736 rounded to seven significant figures, not a different measurement. The square yard is unusual on this site in that respect: the square foot (9.290 304 E−02 m²), square inch (6.4516 E−04 m²) and acre variants are all printed to enough digits to be exact, while the square yard is not. If your calculation needs the eighth digit, square 0.9144 yourself.
The yard also survives in land measurement through the chain: an acre is 22 yd × 220 yd, which is why 43,560 ÷ 9 = 4,840 sq yd per acre exactly.
What is a square foot?
A square foot is the area of a square one foot on each side: 12 in × 12 in = 144 sq in, or 0.09290304 m² exactly (NIST prints 9.290 304 E−02 m²). It is 1/9 of a square yard, and that 1/9 is why square-foot-to-square-yard results so often repeat: 100 sq ft is 11.1111… sq yd, never a clean number.
Nine square feet tile one square yard, which is the picture worth holding onto — a 3 × 3 grid of 1 ft squares.
What shape is a square yard?
| Shape | Dimensions | Check |
|---|---|---|
| Square in feet (the definition) | 3 ft × 3 ft | 3 × 3 = 9 sq ft |
| Square in inches | 36 in × 36 in | 36 × 36 = 1,296 sq in |
| Square in metres | 0.9144 m × 0.9144 m | 0.9144² = 0.83612736 m² |
| Rectangle | 1.5 ft × 6 ft | 1.5 × 6 = 9 |
| Rectangle | 2 ft × 4.5 ft | 2 × 4.5 = 9 |
| Narrow strip | 1 ft × 9 ft | 1 × 9 = 9 |
| Circle of the same area | diameter 3.3851 ft (40.62 in) | √(9 × 4 ÷ π) = 3.38514 |
The 3 × 3 grid is also how a cubic yard is built: 1 cu yd = 27 cu ft = 1 sq yd × 3 ft deep. That is the whole of the depth arithmetic in the next section.
Square yards to cubic yards
Concrete, mulch, topsoil and gravel are sold by the cubic yard, and a cubic yard is a square yard three feet deep. So:
cubic yards = square yards × depth in feet ÷ 3
| Area | Depth | Cubic yards |
|---|---|---|
| 9 sq yd (81 sq ft) | 4 in = 0.3333 ft | 1.00 cu yd |
| 9 sq yd (81 sq ft) | 6 in = 0.5 ft | 1.50 cu yd |
| 45 sq yd (405 sq ft) | 3 in = 0.25 ft | 3.75 cu yd |
| 100 sq yd (900 sq ft) | 4 in = 0.3333 ft | 11.11 cu yd |
| 222.2222 sq yd (2,000 sq ft) | 6 in = 0.5 ft | 37.04 cu yd |
Check the first row the long way: 9 sq yd × 9 = 81 sq ft, × 0.3333 ft = 27 cu ft, ÷ 27 = 1 cu yd. Same answer. For tonnage you also need a material density, which is what the square feet to cubic feet calculator adds.
Where square yards still get used
- Carpet and broadloom flooring — quoted per sq yd in the US even though installers measure rooms in sq ft. Divide the room's sq ft by 9 to compare two quotes on the same footing.
- Concrete and aggregate — ready-mix, sand and gravel are priced per cubic yard, so the area step has to land in sq yd before the depth step.
- Fabric, tarps and roll goods — sold by the yard off a fixed-width roll.
- Topsoil and mulch delivery — sold by the cubic yard; a 3 in mulch depth over 45 sq yd is 3.75 cu yd.
- Older US deeds and UK land records — square yards appear in older plats; the chain-and-yard arithmetic above is why they come out whole.
FAQ
How do I convert square feet to square yards for carpet?
Divide square feet by 9. A 12 ft × 15 ft room is 180 sq ft, which is 20 sq yd. For waste, add the percentage to the area, not to the price: 180 × 1.10 = 198 sq ft = 22 sq yd to order. Rounding the sq yd figure and then adding 10% gives a different answer, so convert first and round last.
Why is 1 square yard equal to 9 square feet and not 3?
A yard is 3 feet, but area scales by the square of the linear factor: 3 ft × 3 ft = 9 sq ft. The same rule makes 1 sq ft = 144 sq in (12 × 12) and 1 sq mi = 27,878,400 sq ft (5,280 × 5,280). Multiplying by 3 instead of 9 is the most common error on this page.
Is the 1/9 factor exact, and why do the decimals repeat?
1 sq yd = 9 sq ft is exact and definitional, because 1 yd = 3 ft is exact. The reverse factor 1/9 = 0.111111… is exact as a fraction but non-terminating in base 10, which is why the converter shows 11.1111 sq yd for 100 sq ft rather than a clean number. Prefer dividing by 9 over multiplying by 0.1111111111111111: the division is exact, the truncated decimal is not.
How many square yards are in an acre or a square mile?
1 acre = 4,840 sq yd (43,560 ÷ 9), which is also the historical definition, since an acre is 22 yd × 220 yd. 1 sq mi = 3,097,600 sq yd (27,878,400 ÷ 9). 1 hectare = 11,959.900463 sq yd, which is not whole because the hectare is defined in metres.
How do I turn a square-yard area into cubic yards of concrete or mulch?
Cubic yards = square yards × depth in feet ÷ 3, because 1 cu yd = 27 cu ft = 1 sq yd × 3 ft deep. So 9 sq yd at 4 in (1/3 ft) deep is 9 × 0.3333 ÷ 3 = 1 cu yd, the same as 81 sq ft at 4 in = 27 cu ft. See the sq ft to cubic feet calculator to get the tonnage from a density.
How many square metres are in a square yard?
0.83612736 m² exactly, because 1 yd = 0.9144 m exactly and 0.9144 squared = 0.83612736. NIST SP 811 prints this as 8.361 274 E−01, which is the same number rounded to seven significant figures; if you need the last digits, square 0.9144 yourself rather than using the printed factor.
Sources and How to Check This Page
- Area factors — square yard 8.361 274 E−01 m², square foot 9.290 304 E−02 m², square inch 6.4516 E−04 m², acre (based on U.S. survey foot) 4.046 873 E+03 m², square mile 2.589 988 E+06 m² — are transcribed from NIST Special Publication 811, Appendix B.9.1. The rounding of the square-yard factor to seven significant figures is visible in that table and is discussed above.
- 1 ft = 0.3048 m exactly, from which 1 yd = 0.9144 m and 1 in = 0.0254 m follow, is stated in 85 FR 62698, FR Doc. 2020-21902, which names the 1959 notice at 24 FR 5348 as the definition's origin.
- The acre as 22 yd × 220 yd, 43,560 sq ft, 4,840 sq yd, 160 square rods, and 66 ft = 1 chain comes from the BLM Land Description Diagram.
- Every other number here is arithmetic on those factors and can be re-derived: 180 ÷ 9 = 20; 180 × 1.10 = 198 and 198 ÷ 9 = 22; 43,560 ÷ 9 = 4,840; 27,878,400 ÷ 9 = 3,097,600; 0.9144² = 0.83612736; 36² = 1,296; √(9 × 4 ÷ π) = 3.38514; 9 × 0.3333 ÷ 3 = 1.0; 2,000 ÷ 9 × 0.5 ÷ 3 = 37.04.
- What this page does not claim: carpet prices, roll widths as an industry standard, or a universal waste percentage. The 10% in the table above is a worked assumption, not a recommendation — patterned carpet, diagonal layouts and seamed rooms need more, and a rectangular room cut from a roll that fits may need none. The 12 ft roll sentence is arithmetic on an assumed width, not a statement about any supplier.