This rounding calculator rounds any number to the place value you choose — nearest whole number, tenth, hundredth, thousandth, ten, hundred, thousand — or to 1–4 significant figures. Pick the rounding mode too: standard half up (5 rounds up), half down, floor (always down), or ceiling (always up).
You also get a table showing your number rounded to every nearby precision at once, which makes it a quick round to the nearest hundredth calculator, a round to 2 decimal places tool, and a significant figures calculator in one. The difference row shows exactly how much rounding changed your number.
Rounding Rules: When Does 5 Round Up?
The standard rule taught in school is round half up: look at the digit one place beyond where you are rounding — if it is 5 or more, round up; if it is 4 or less, round down.
- 3.14159 to 2 decimal places → 3.14 (next digit is 1, round down).
- 2.675 to the nearest hundredth → 2.68 (next digit is 5, round up).
- 1,250 to the nearest hundred → 1,300 with half up, but 1,200 with half down.
The other modes have specific uses: floor always drops toward negative infinity (used for “complete units” like full boxes), ceiling always rises (used for “how many containers do I need”), and half down is the mirror of the standard rule. Accountants also use banker’s rounding, where a tie of exactly 5 goes to the nearest even digit to avoid systematic upward bias.
Significant Figures Explained
Rounding to significant figures keeps a fixed number of meaningful digits rather than a fixed decimal place, which is why science classes use it.
- All non-zero digits are significant: 3.14159 to 3 sig figs → 3.14.
- Leading zeros are not significant: 0.004521 to 2 sig figs → 0.0045.
- Large numbers round in their leading places: 52,764 to 2 sig figs → 53,000.
- Trailing zeros after rounding matter: 2.997 to 2 sig figs → 3.0, not just 3.
The rule of thumb in lab work: your answer should carry as many significant figures as the least precise measurement that went into it. This significant figures calculator handles 1 to 4 sig figs, which covers nearly all homework and lab-report cases.
Worked Example: Rounding 3.14159 Every Way
Take pi to five decimals, 3.14159, with standard half-up rounding:
- Nearest whole number → 3
- Nearest tenth → 3.1 (next digit 4, round down)
- Nearest hundredth → 3.14 (next digit 1, round down)
- Nearest thousandth → 3.142 (next digit 5, round up)
- 2 significant figures → 3.1
Now a bigger number, 2,675, rounded to the nearest hundred: the tens digit is 7, so it rounds up to 2,700. With floor mode it would be 2,600 regardless, and with ceiling mode 2,700 even if the tens digit were 1. Same number, three defensible answers — which is why stating your rounding method matters on anything that gets checked.
Frequently Asked Questions
How do you round 2.675 to the nearest hundredth?
2.675 rounds to 2.68 at the nearest hundredth, because the digit being dropped is 5 and standard rounding sends 5 up. Watch out: many calculators and programming languages answer 2.67, because computers store 2.675 as 2.67499999… in binary floating point. This calculator corrects for that error and returns the mathematically right 2.68.
What is 3.14159 rounded to the nearest hundredth?
3.14159 rounded to the nearest hundredth is 3.14. Look at the thousandths digit, which is 1; since it is less than 5, the hundredths digit stays at 4 and everything after it is dropped. To the nearest thousandth the answer is 3.142, because the next digit there is a 5, which rounds up.
Does 5 round up or down?
Under the standard “half up” rule used in schools, 5 always rounds up: 4.5 becomes 5, and 0.25 to one decimal place becomes 0.3. But it is a convention, not a law — banker’s rounding (round half to even) sends 4.5 to 4 and 5.5 to 6, and is used in accounting and by default in Python, to keep long sums from drifting upward.
How do you round to 2 significant figures?
Keep the first two non-zero digits, round the second one based on the digit after it, and replace the rest with zeros or drop them. So 52,764 → 53,000; 0.004521 → 0.0045; and 2.997 → 3.0. Leading zeros never count as significant figures, but the trailing zero in 3.0 does — it shows your precision.
What is banker’s rounding?
Banker’s rounding, or round half to even, breaks exact ties by rounding to the nearest even digit: 2.5 → 2, 3.5 → 4, 2.45 → 2.4 at one decimal. Ordinary half-up rounding pushes every tie upward, which inflates large sums of rounded values; ties split between up and down cancel that bias, which is why financial systems and IEEE 754 floating point use it.