Rounding calculator guide
Rounding replaces a number with a nearby value that has fewer digits. Two different jobs share the same tool. Positive precision is decimal-place rounding: precision 2 keeps hundredths (money-style cents), precision 1 keeps tenths, and precision 0 keeps the nearest whole number. Negative precision is place-value rounding: −1 is the nearest 10, −2 the nearest 100, −3 the nearest 1,000. The two look similar because both scale the number by a power of ten, apply a nearest-integer step, then scale back — only the sign of the exponent changes.
This calculator uses JavaScript Math.round, which breaks exact halfway cases toward +Infinity. That is “half up” on the number line, not “5 always away from zero.” Positive halves go up (0.5 → 1, 1.5 → 2) and negative halves go toward zero (−0.5 → 0, −1.5 → −1). That is not banker’s rounding (round-to-even) and is not the NIST SP 811 even-digit tie rule. Enter a number, an integer precision from −6 to 15, and select Calculate.
How to use this rounding calculator
- Enter the number: Type the value to round, for example 123.4567 or −1.5. Empty, non-numeric, and non-finite inputs are rejected.
- Enter the precision: Type an integer from −6 to 15. Use 2 for hundredths, 0 for the nearest whole number, and a negative integer for a place value.
- Read the negative-precision hint: Under the precision field, −1 means nearest 10, −2 nearest 100, and −3 nearest 1,000. Precision 0 is the nearest whole number.
- Select Calculate: Press Calculate to round. Invalid number or precision values produce an error instead of a result.
- Compare original and rounded values: The large figure is the rounded number. The original input and a place label such as “2 decimal places” or “nearest 10” appear underneath.
- Reset or share: Reset restores the example 123.4567 at precision 2 (which rounds to 123.46). Copy the link to share the current number and precision.
Formula and variables
Decimal-place rounding multiplies by 10^p so the rounding digit sits in the ones place, applies Math.round, then divides by the same power. Place-value rounding divides by 10^{−p} first (10, 100, 1,000, …) so the ones digit of that scaled value is the place being rounded, then multiplies back. Math.round(x) is the integer closest to x, with exact halves taken toward +Infinity — the ECMAScript rule, not IEEE 754 roundTiesToEven.
p ≥ 0: round(n, p) = Math.round(n × 10^p) / 10^p p < 0: round(n, p) = Math.round(n / 10^{−p}) × 10^{−p}- n — Original number
- The finite real number to round, entered as a decimal. (unitless)
- p — Precision
- An integer from −6 to 15. Non-negative p is decimal places; negative p rounds to 10^{−p}. (integer)
- 10^p — Scale factor
- For p ≥ 0, the multiplier that shifts the rounding digit into the ones place. (power of ten)
- Math.round — Nearest integer (half toward +∞)
- JavaScript nearest-integer function: 0.5 → 1 and −1.5 → −1. (unitless integer)
Worked example: round 123.4567 to 2 decimal places
The default inputs round 123.4567 to hundredths. The same scale-and-round method then rounds 127 to the nearest 10 and shows how a negative half is treated.
- Number
- 123.4567
- Precision
- 2
- Precision 2 ≥ 0, so this is decimal-place rounding: multiply by 10^2 = 100.
- 123.4567 × 100 = 12345.67. The digit after the rounding position is 6, which is greater than 5, so Math.round(12345.67) = 12346.
- Divide by 100: 12346 / 100 = 123.46. The place label is “2 decimal places.”
- Same method at precision 1 on 123.45: 123.45 × 10 = 1234.5, and Math.round(1234.5) = 1235 because the half goes toward +Infinity, so 123.5.
- Place-value example: 127 at precision −1. Divide by 10^{1} = 10 to get 12.7; Math.round(12.7) = 13; multiply back by 10 to get 130 (“nearest 10”).
- Half toward +Infinity on a negative: −1.5 at precision 0 is Math.round(−1.5) = −1, not −2.
Result: 123.4567 rounded to 2 decimal places is 123.46
The third decimal digit is 6, so the hundredths digit 5 increases to 6. The same engine with precision −1 on 127 yields 130, and with precision 0 on −1.5 yields −1 because a tie is taken toward +Infinity rather than away from zero.
Understanding your results
Original and rounded values
The original is the parsed input. The rounded value is the nearest number at the requested precision under Math.round. When precision is positive, trailing zeros are kept in the display so two decimal places still reads as hundredths (for example 12.50).
Place label
The label names the rounding target in words: “2 decimal places,” “1 decimal place,” “nearest whole number” at precision 0, “nearest 10” at −1, and “nearest 100” at −2. Use it to confirm that a negative precision was interpreted as a place value rather than as an error.
Half toward +Infinity
When the discarded part is exactly 5 followed only by zeros, Math.round steps to the next integer in the positive direction. That matches everyday “5 or more, round up” for positive numbers and disagrees with “round 5 away from zero” for negatives. −1.5 to the nearest whole number is −1 here, not −2.
Assumptions
- Rounding uses JavaScript Math.round: exact halves go toward +Infinity (0.5 → 1, −1.5 → −1).
- Precision is an integer in [−6, 15]. Non-integers, empty strings, and values outside that range are rejected.
- The number must be a finite decimal; empty, non-numeric, and infinite inputs are rejected.
- Positive precision counts decimal places; negative precision rounds to 10, 100, 1,000, …; precision 0 is the nearest whole number.
- The calculation is a single rounding step from the original number, never a chain of intermediate roundings.
Limitations
- This is not banker’s rounding and not NIST SP 811 round-to-even. An exact 5 is never sent to the nearest even digit.
- Significant-figure rounding (keep k leading digits regardless of place) is outside the scope of this calculator.
- IEEE-754 binary floating point can miss an exact decimal half: 1.005 × 100 is slightly under 100.5, so 1.005 to 2 decimal places can return 1.00 rather than 1.01.
- Truncation (dropping extra digits without looking at the next one) is a different operation and is not offered here.
- Precision outside −6 to 15 is rejected so the scale factor stays within a range where decimal-place rounding is meaningful in double precision.
Common mistakes
- Rounding in stages: 2.349 to the nearest tenth is 2.3 (look only at the 4), not 2.4 from 2.349 → 2.35 → 2.4.
- Assuming −1.5 rounds to −2. School “round 5 away from zero” would do that; this calculator follows Math.round toward +Infinity, so −1.5 → −1.
- Treating negative precision as invalid. Precision −1 is nearest 10; it is not “minus one decimal place” in the sense of adding digits.
- Confusing rounding with truncation. 3.78 to one decimal place is 3.8 when rounded and 3.7 when truncated.
- Expecting NIST or IEEE round-to-even on a trailing 5. 2.5 to a whole number is 3 here, not 2.
- Choosing more decimal places than the measurement supports — reporting 12.3456 inches when the ruler was marked in inches implies false precision.
Practical use cases
Money and two decimal places
Currency is almost always rounded to hundredths. Precision 2 on 47.386 gives 47.39, matching the usual cents rule for a positive amount. Confirm the halfway rule before using this on negative balances.
Estimation to a place value
Precision −1 or −2 is the nearest 10 or 100, which is the mental-math form of rounding used to check whether a product or a total is in the right ballpark (127 → 130, 8,461 → 8,500).
Measurements and reported precision
Match precision to the instrument: nearest whole number for counts, one decimal for many classroom measurements, two decimals for typical SI millimetre-to-centimetre reporting.
Homework checks of the halfway case
Use 0.5, 1.5, −0.5, and −1.5 at precision 0 to see half toward +Infinity in both directions, then compare with a textbook that rounds 5 away from zero.
Planning and decision guide
Round once, from the original number
Identify the place, look at the single digit immediately to its right, and round in one step. Intermediate rounding changes which digit is the decider and is the most common source of a “wrong” textbook answer.
Pick decimal places or place value on purpose
If the question says “to two decimal places” or “to the nearest hundredth,” use p = 2. If it says “to the nearest ten,” use p = −1. Mixing those two phrasings is how 347 rounded to tens becomes 350, not 347.00.
Know which halfway rule your context needs
Statistics and some laboratory standards prefer round-to-even (NIST SP 811 Appendix B.7.1, IEEE 754) because it avoids a systematic upward drift. Cash rounding, many school rules, and this calculator’s JavaScript engine do not. If a specification says “round half even,” do not use these results for the tie cases.
Frequently asked questions
What rounding rule does this calculator use?
JavaScript Math.round: the nearest value at the chosen precision, with exact halves taken toward +Infinity. 0.5 to a whole number is 1; −1.5 to a whole number is −1. It is half-up on the number line, not banker’s rounding.
Why does −1.5 round to −1 instead of −2?
Toward +Infinity from −1.5 is −1. A rule that always sends 5 away from zero would give −2, and round-to-even would also give −2 because −2 is even. This calculator documents the ECMAScript choice rather than either of those conventions.
What does a negative precision mean?
It rounds to a place value rather than to decimal places. Precision −1 is the nearest 10 (127 → 130), −2 the nearest 100, −3 the nearest 1,000. Precision 0 is the nearest whole number.
What is the difference between decimal-place rounding and place-value rounding?
Decimal-place rounding (p ≥ 0) keeps a stated number of digits after the decimal point: p = 2 on 123.4567 is 123.46. Place-value rounding (p < 0) moves left of the decimal: p = −1 on 127 is 130. Both use the same Math.round step after scaling by a power of ten.
Is this the same as NIST SP 811 or banker’s rounding?
No. NIST SP 811 Appendix B.7.1 (and IEEE 754 roundTiesToEven) send an exact leftover 5 to the nearest even retained digit. This calculator never does that: 2.5 becomes 3, not 2. Cite NIST when a specification requires even rounding; use this tool when you want JavaScript half toward +Infinity.
How is rounding different from truncating?
Rounding looks at the next digit and may increase the kept digit. Truncating drops extra digits with no adjustment. 3.78 to one decimal place is 3.8 rounded and 3.7 truncated.
Why is precision limited to −6 through 15?
Those bounds cover everyday decimal places (up to 15, near the limit of double-precision significance) and place values from tens through millions. Values outside the range are rejected instead of producing a scale factor that cannot be represented cleanly.
Should I round 2.349 to 2.4 if I first round to two decimals?
No. To the nearest tenth, look only at the hundredths digit 4, so 2.349 → 2.3. The chain 2.349 → 2.35 → 2.4 is a different — and incorrect — procedure for a single requested place.
Sources and review
- Rounding — MathWorld — A Wolfram Resource. Accessed 2026-08-23.
- NIST Guide to the SI, Appendix B.7: Rules for rounding numbers — National Institute of Standards and Technology (NIST). Accessed 2026-08-23.
- Rounding Numbers — Math Is Fun. Accessed 2026-08-23.
Reviewed 2026-08-23.