Inputs
Scientific notation allowed, e.g.,
1e6. Negative inputs are non‑real.
Output rounding shown by the badge mode and decimal selection.
Results
Half Up · 2 decimals| # | Input x | √x (raw) | Rounded |
|---|---|---|---|
| No results yet. Click Calculate. | |||
Tip: Click CSV or PDF after calculating. Data include inputs, raw roots, and rounded values.
Step Explanations
- Steps will appear here after you calculate.
Example Data (mode: Half Up, 2 decimals)
| Input x | √x | Rounded (2dp) |
|---|---|---|
| 2 | 1.4142135623730951 | 1.41 |
| 3 | 1.7320508075688772 | 1.73 |
| 5 | 2.23606797749979 | 2.24 |
| 10 | 3.1622776601683795 | 3.16 |
| 50 | 7.0710678118654755 | 7.07 |
| 0.5 | 0.7071067811865476 | 0.71 |
| 2.25 | 1.5 | 1.50 |
| 100 | 10 | 10.00 |
| 1e6 | 1000 | 1000.00 |
| 123456789 | 11111.111060555555 | 11111.11 |
You can load these into the input box using the button above.
Formula Used
Square root: For a non‑negative real number x, the principal square root is y such that y2 = x, written as √x.
Decimal rounding to d places: compute z = √x, then apply your selected rule to z × 10d and divide back by 10d. Supported rules:
- Half Up: halves go away from zero, others to nearest.
- Half Even: halves go to the nearest even last digit.
- Floor: toward −∞ at the given precision.
- Ceil: toward +∞ at the given precision.
- Truncate: toward 0 at the given precision.
Note: Floating‑point arithmetic can introduce tiny representation errors; critical work should use arbitrary‑precision libraries.
How to Use
- Paste or type values into the input box.
- Select decimal places and a rounding mode.
- Click Calculate. Review the results table and steps.
- Export your table using Download CSV or Download PDF.
- Use Load Example Data to try the sample set.
Common Square Roots (1–25)
Rounded to 2 decimals · Mode: Half Up| n | √n (raw) | Rounded |
|---|
Rounding Modes Side‑by‑Side
Decimals: 2| Input x | √x (raw) | Half Up | Half Even | Floor | Ceil | Truncate |
|---|
FAQs
Half Up pushes exact half cases away from zero. Half Even pushes exact half cases toward the nearest even last digit, reducing cumulative bias in large datasets.
The principal square root is defined for non‑negative inputs only. Negative inputs will be marked as non‑real and skipped in the results.
You can choose from 0 to 10 decimal places. For highly sensitive work, consider higher‑precision math libraries to minimize floating‑point rounding artifacts.
Different tools use different rounding rules and precision. Ensure you match both the rounding mode and decimal places when comparing results across tools.
Yes. Use the CSV button for spreadsheets or the PDF button for a formatted document containing your table and selections.