Round any number to a specified number of decimal places or significant figures using multiple rounding methods — standard, half-up, half-down, floor, ceiling, and truncate.
| Method | Description |
|---|---|
| Standard / Half-up | Round half away from zero (most common) |
| Half-down | Round half toward zero |
| Half-even (Banker's) | Round half to nearest even digit |
| Floor | Always round down |
| Ceiling | Always round up |
| Truncate | Remove extra digits without rounding |
| Method | Result |
|---|---|
| Standard (Half-up) | 3.14 |
| Half-down | 3.14 |
| Half-even (Banker's) | 3.14 |
| Floor (round down) | 3.14 |
| Ceiling (round up) | 3.15 |
| Truncate | 3.14 |
Round 12.5 to a whole number and this calculator shows 13 in the Standard and Ceiling rows, but 12 in the half-down, half-even, floor and truncate rows. None of those is a bug. The methods only disagree when a value sits exactly on the midpoint or when you push it in one direction, and seeing them lined up tells you which convention your spreadsheet, invoice or lab report is quietly using. A second tab rounds to significant figures instead of decimal places.
Take 0.125 and round it to 2 decimal places. The calculator first slides the decimal point two places to the right: 0.125 × 10² = 12.5.
Every method now has to pick a whole number from 12.5 and slide back. In plain form the rule is result = pick(n × 10^d) ÷ 10^d, where d is the number of decimal places and pick is half-up, half-down, half-even, floor, ceiling or truncate.
Line by line: Standard gives 13 ÷ 100 = 0.13. Half-down gives 0.12. Half-even, also called banker's rounding, gives 0.12 because 12 is the even neighbour of 12.5. Floor gives 0.12, ceiling gives 0.13 and truncate gives 0.12. The page drops trailing zeros, so a result of 1.00 is displayed as 1.
The Significant Figures tab shifts by a different amount: factor = 10^(sf − 1 − floor(log10|n|)). For 0.000456789 at 3 figures the exponent is 3 − 1 − (−4) = 6, so 0.000456789 × 10⁶ = 456.789, which rounds to 457. Dividing back gives 0.000457, and the scientific-notation card shows 4.57e-4.
One limit comes from how computers store decimals. 1.005 is held as a value slightly below 1.005, so at 2 places every row returns 1 except ceiling, which returns 1.01. In the same way 2.675 shows 2.67 in the Standard row, although most people would round it to 2.68 by hand.
Standard (half-up) is the usual convention on invoices and tax forms, but some accounting software, and the built-in round() in languages such as Python, use half-even instead. Check which rule the other party applies, because over thousands of lines the two can differ by real money.
Half-even sends exact ties to the neighbour with an even last digit, so 0.125 goes down to 0.12 but 0.375 goes up to 0.38. Ties then round up about half the time and down about half the time, which stops a long column of figures from drifting upward.
Only for positive numbers. At 0 places, -2.5 floors to -3 but truncates to -2. Treat the half-down row with care on negatives: it returns -3 for -2.5 on this page, which is away from zero rather than toward it.
The binary number closest to 1.005 is a hair under it, so it is not truly a tie and every rule that looks at the stored value rounds it down. Ceiling is the exception, which is why it alone shows 1.01.
Not in the Rounded Value card, where 1.2 at 3 figures shows as 1.2. The scientific-notation card keeps them and prints 1.20e+0, which is the form to copy into a lab report that needs to show three figures.