Rounding and Significant Figures Calculator
Round a number to a chosen number of decimal places or significant figures. Also gives the value rounded up
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates rounded to the nearest, rounded up to those places, rounded down to those places and 2 more results from number, decimal places and significant figures. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Round only the final answer, not the steps in between, or the rounding errors add up. Quote a result to no more significant figures than the least precise input supports. For the effect of a reading error see the percentage error calculator, and for the spread of repeated readings see the standard deviation calculator.
Cross-check: 37 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 37 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Number | 1,234.5678 |
| Decimal places | 2 |
| Significant figures | 3 |
- To 2 decimal places: 1,234.5678 → 1,234.57 (nearest), 1,234.57 (up), 1,234.56 (down), 1,234.56 (truncated)
- To 3 significant figures: 1,234.5678 → 1,230
- Rounding error to 2 places = |1,234.57 − 1,234.5678| = 0.0022
Assumptions
- Halves round away from zero (2.5 gives 3 and −2.5 gives −3), the usual school and engineering rule, not the round-half-to-even rule some software uses
- The number is rounded as written, so 1.005 to two places is 1.01 even though the nearest binary number is slightly below 1.005
- Decimal places and significant figures are rounded separately from the original number, not one after the other
- Rounded up and rounded down follow the number line, so −2.3 rounded up to a whole number is −2 and rounded down is −3
- Rounding to significant figures can give a value with trailing zeros that are not shown, so 1,234.5678 to three figures is 1,230
Round only the final answer, not the steps in between, or the rounding errors add up. Quote a result to no more significant figures than the least precise input supports. For the effect of a reading error see the percentage error calculator, and for the spread of repeated readings see the standard deviation calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Number | (number) | -1.000e15 or more, up to 1.000e15 | The value to round, up to 15 digits. |
| Decimal places | (number) | -6 or more, up to 15 | A whole number from −6 to 15. Use 0 for the nearest whole number, 2 for hundredths, −1 for the nearest ten, −2 for the nearest hundred. |
| Significant figures | (number) | 1 or more, up to 15 | A whole number from 1 to 15. Leading zeros are not significant: 0.00456 has three significant figures. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Rounded to the nearest (decimal places) | (number) | Shown to 15 decimal places | |
| Rounded up (toward +∞) to those places | (number) | Shown to 15 decimal places | |
| Rounded down (toward −∞) to those places | (number) | Shown to 15 decimal places | |
| Truncated (toward zero) to those places | (number) | Shown to 15 decimal places | |
| Rounded to significant figures | (number) | Shown to 15 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with number
| Number | Rounded to the nearest | Rounded up | Rounded down |
|---|---|---|---|
| 123 | 123 | 123 | 123 |
| 309 | 309 | 309 | 309 |
| 617 | 617 | 617 | 617 |
| 1,230 | 1,230 | 1,230 | 1,230 |
| 2,470 | 2,470 | 2,470 | 2,470 |
| 4,940 | 4,940 | 4,940 | 4,940 |
| 12,300 | 12,300 | 12,300 | 12,300 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter number, decimal places and significant figures. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Halves round away from zero (2.5 gives 3 and −2.5 gives −3), the usual school and engineering rule, not the round-half-to-even rule some software uses. The number is rounded as written, so 1.005 to two places is 1.01 even though the nearest binary number is slightly below 1.005. Decimal places and significant figures are rounded separately from the original number, not one after the other. Rounded up and rounded down follow the number line, so −2.3 rounded up to a whole number is −2 and rounded down is −3. Rounding to significant figures can give a value with trailing zeros that are not shown, so 1,234.5678 to three figures is 1,230.
Which calculators should I use next?
Common next steps are Percentage Calculator, Percentage Error, Standard Deviation and Variance and Ratio Calculator. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 37 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Percentage, Ratio and Rounding Formulas: Formulas for percentage, percentage change, ratios, proportions, decimal places and significant figures
- Measurement Uncertainty Formulas: Measurement uncertainty formulas: the standard uncertainty of a rectangular limit
- Mean and Standard Deviation Formulas: Statistics formulas for test readings: mean, median, mode, range, standard deviation, variance and standard error
More Engineering Mathematics calculatorsAll engineering calculatorsRounding and Significant Figures in Elecmetric