Round to the Nearest Thousandth Calculator
Enter a number and instantly get it rounded to the nearest thousandth (0.001 — three decimal places), with the floor and ceiling thousandths, the rounding error, and the deciding digit shown on a number line.
Third decimal place — ten-thousandths digit 0–4 rounds down, 5–9 rounds up
- 1
Multiply by 1,000
3.14159 × 1000 = 3,141.59 - 2
Round to nearest integer
round(3,141.59) = 3,142Ten-thousandths digit 0–4 rounds down, 5–9 rounds up. - 3
Divide back by 1,000
3,142 ÷ 1000 = 3.142
How does this calculator work?
Multiply by 1,000, round to the nearest integer (4 and below stay, 5 and above go up), then divide by 1,000. The fourth decimal digit is the deciding digit. Rounding 3.14159 gives 3.142; rounding 2.71828 gives 2.718.
Formula
How this is calculated
Rounding to the nearest thousandth means keeping three digits after the decimal point. The method is: multiply the number by 1,000 to shift the decimal three places right, apply standard half-up rounding to get an integer, then divide by 1,000 to shift back. The ten-thousandths digit — the fourth decimal place — is the deciding digit: 0 through 4 leave the thousandths digit unchanged (round down), while 5 through 9 increase it by one (round up).
For example, 3.14159 has a ten-thousandths digit of 5, so it rounds up to 3.142. Conversely, 2.71828 has a ten-thousandths digit of 2, so it rounds down to 2.718. The rounding error is the absolute difference between the original and the rounded value; it is always between 0 and 0.0005.
A known limitation: floating-point arithmetic cannot represent every decimal fraction exactly in binary, so a tiny residual (often around 10⁻¹⁶) can occasionally make a borderline value round unexpectedly. For instance, 1.0005 may be stored internally as 1.000499999…, causing it to round down to 1.000 instead of up to 1.001. If exact-decimal precision is essential, use a decimal-arithmetic library.
Frequently asked questions
The thousandths place is the third digit to the right of the decimal point. In 3.14159, the tenths digit is 1, the hundredths digit is 4, the thousandths digit is 1, and the ten-thousandths digit is 5.
The ten-thousandths digit is 8, which is ≥ 5, so round up: 2.7185 becomes 2.719.
Yes — a thousandth is 0.001, which is always expressed with exactly three decimal places. The two phrases mean the same thing.
Also known as
TG we-Calculate Editorial Team. (2026). Round to the Nearest Thousandth Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/round-to-the-nearest-thousandth-calculator
TG we-Calculate Editorial Team. "Round to the Nearest Thousandth Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/round-to-the-nearest-thousandth-calculator.
TG we-Calculate Editorial Team, "Round to the Nearest Thousandth Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/round-to-the-nearest-thousandth-calculator
@misc{wecalculate_round_to_the_nearest_thousandth_calculator, title = {Round to the Nearest Thousandth Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/round-to-the-nearest-thousandth-calculator}}, year = {2026}, note = {TG we-Calculate} }
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