Rounding Calculator
Round numbers to specified decimal places or nearest place values.
Half-up, half-even, and why banks differ
Rounding replaces a number with a nearby simpler one. The familiar school rule isround half up: look at the digit after your cut-off, round up if it is 5 or more, down otherwise. It is simple and it has a bias — halves always go the same direction, so summing many rounded values drifts upward.
Banker's rounding, or round half to even, fixes that by sending exact halves to the nearest even digit: 2.5 becomes 2, 3.5 becomes 4. Across many values the ups and downs cancel, so totals stay unbiased. It is the IEEE 754 default, which means it is what most programming languages and spreadsheets do by default — a frequent source of surprise when a total disagrees with a hand-check by a penny.
Two practical points. Round once, at the end — rounding intermediate results and then rounding again compounds the error, and can shift a final figure by more than a full unit. And significant figures are not decimal places: 0.004567 to three significant figures is 0.00457, while to three decimal places it is 0.005. Which one a specification means changes the answer substantially for small numbers.
Frequently Asked Questions
How does standard rounding work?
If the digit following your target precision is 5 or greater, round up. If less than 5, round down.
What are the different rounding rules?
Half-up rounds 0.5 away from zero and is what most people learn. Half-even - banker's rounding - rounds 0.5 to the nearest even digit, so 2.5 becomes 2 and 3.5 becomes 4. Half-even is the IEEE 754 default because it avoids the upward bias that half-up introduces across large data sets.
What is the difference between significant figures and decimal places?
Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. 0.004567 has 6 decimal places but 4 significant figures. Scientific work uses significant figures because they express measurement precision, which decimal places do not.
Why does rounding twice give the wrong answer?
Because each rounding discards information. Rounding 2.44 to 2.4 and then to 2 loses the fact that it was below the midpoint, whereas rounding 2.44 directly gives 2 as well - but 2.46 to 2.5 to 3 differs from 2.46 straight to 2. Always round once, from the original value.