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Powers & roots of any number
Squares, cubes, and both roots — instantly.
MATH REFERENCE
Squares, Cubes & Roots Chart
Every square, cube, square root, and cube root from 1 to 30 in one printable chart — plus a live calculator for any number up to 1,000.
Why memorize squares when you can look them up
Squaring a number means multiplying it by itself (7² = 7 × 7 = 49); cubing means three copies (7³ = 7 × 7 × 7 = 343). Roots undo the operation: √49 = 7 because 7² = 49, and ∛343 = 7 because 7³ = 343. The chart below covers the 1–30 range where almost all everyday questions land — test scores, recipe scaling, tile and flooring math, and back-of-the-envelope physics. Enter anything up to 1,000 in the calculator for the rest.
A worked example
Take 7. Square: 7 × 7 = 49. Cube: 49 × 7 = 343. Square root: √7 ≈ 2.6458 — check it: 2.6458 × 2.6458 ≈ 7. Cube root: ∛7 ≈ 1.9129 — check: 1.9129³ ≈ 7. Roots of non-perfect powers are irrational, so the chart rounds them to 4 decimals — plenty for real-world use.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Square | n × n | Area of a square with side n — the workhorse of area math. |
| Cube | n × n × n | Volume of a cube with edge n. |
| Square root | √n | The side length whose square is n. |
| Cube root | ∛n | The edge length whose cube is n. |
Full chart: 1 to 30
| n | n² | n³ | √n | ∛n |
|---|---|---|---|---|
| 1 | 1 | 1 | 1.0000 | 1 |
| 2 | 4 | 8 | 1.4142 | 1.2599 |
| 3 | 9 | 27 | 1.7321 | 1.4422 |
| 4 | 16 | 64 | 2.0000 | 1.5874 |
| 5 | 25 | 125 | 2.2361 | 1.7100 |
| 6 | 36 | 216 | 2.4495 | 1.8171 |
| 7 | 49 | 343 | 2.6458 | 1.9129 |
| 8 | 64 | 512 | 2.8284 | 2 |
| 9 | 81 | 729 | 3.0000 | 2.0801 |
| 10 | 100 | 1000 | 3.1623 | 2.1544 |
| 11 | 121 | 1331 | 3.3166 | 2.2240 |
| 12 | 144 | 1728 | 3.4641 | 2.2894 |
| 13 | 169 | 2197 | 3.6056 | 2.3513 |
| 14 | 196 | 2744 | 3.7417 | 2.4101 |
| 15 | 225 | 3375 | 3.8730 | 2.4662 |
| 16 | 256 | 4096 | 4.0000 | 2.5198 |
| 17 | 289 | 4913 | 4.1231 | 2.5713 |
| 18 | 324 | 5832 | 4.2426 | 2.6207 |
| 19 | 361 | 6859 | 4.3589 | 2.6684 |
| 20 | 400 | 8000 | 4.4721 | 2.7144 |
| 21 | 441 | 9261 | 4.5826 | 2.7589 |
| 22 | 484 | 10648 | 4.6904 | 2.8020 |
| 23 | 529 | 12167 | 4.7958 | 2.8439 |
| 24 | 576 | 13824 | 4.8990 | 2.8845 |
| 25 | 625 | 15625 | 5.0000 | 2.9240 |
| 26 | 676 | 17576 | 5.0990 | 2.9625 |
| 27 | 729 | 19683 | 5.1962 | 3 |
| 28 | 784 | 21952 | 5.2915 | 3.0366 |
| 29 | 841 | 24389 | 5.3852 | 3.0723 |
| 30 | 900 | 27000 | 5.4772 | 3.1072 |
Who uses this
- Students: perfect squares through 30² = 900 show up constantly in algebra, geometry, and standardized tests.
- DIYers and crafters: scaling a pattern or a recipe by area uses squares; scaling a box or planter by volume uses cubes.
- Programmers: powers of two are everywhere in computing — spot 64, 256, and 1,024 in the cubes column's neighborhood.
- Puzzle solvers: crossword and trivia answers love "what is 13 squared" — 169, since you asked.
Accuracy & limitations
Squares and cubes of whole numbers are exact — every digit in the chart is correct. Roots of non-perfect powers are irrational and shown rounded to 4 decimals, which is far tighter than any tape measure or kitchen scale. The calculator accepts 1 to 1,000; beyond that, split the number into a coefficient and a power of ten and work each part separately.
Base conversions more your thing? The binary, hex & decimal chart covers 0–255 in four bases.
Cite this calculatorBright Side Kit. “Squares, Cubes & Roots Chart.” brightoolbox.com, 2026.
Bright Side Kit. "Squares, Cubes & Roots Chart." https://brightoolbox.com/squares-cubes-roots-chart/ Accessed October 22, 2026.Frequently asked questions
What is 12 squared?
144 — 12 × 12. It is one of the most-looked-up squares because 12 shows up in dozens, feet, and egg cartons. The chart above has all squares through 30² = 900.
What is the cube root of 27?
3 — because 3 × 3 × 3 = 27. Perfect cubes in the 1–30 range are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000, 1,331, 1,728, 2,197, 2,744, 3,375, 4,096, 4,913, 5,832, 6,859, 8,000, 9,261, 10,648, 12,167, 13,824, 15,625, 17,576, 19,683, 21,952, 24,389, and 27,000 — all exact in the chart.
How do you find a square root by hand?
Use the guess-and-refine method: to find √50, guess 7 (7² = 49, close), then refine with 50 ÷ 7 ≈ 7.14 and average: (7 + 7.14) ÷ 2 = 7.07. Square it: 7.07² ≈ 49.98 — good enough. Repeat for more digits, or just use the calculator above.
What is the difference between a square and a square root?
They are inverses. Squaring multiplies a number by itself (9² = 81); the square root asks which number, squared, gives the original (√81 = 9). Same pair, opposite directions — like doubling and halving.
Why are square numbers called 'square'?
Because n² is the area of a square with side n: 5² = 25 is literally a 5-by-5 square of unit tiles. Cubes are named the same way — n³ is the volume of an n-by-n-by-n cube.
What is 15 cubed?
3,375 — 15 × 15 × 15. Cubes grow fast: 15³ is already over three thousand while 15² is only 225.
Is the square root of a negative number real?
No — no real number squared gives a negative. √(−4) is imaginary (2i). This chart and calculator stick to real numbers: enter 1 to 1,000.