π Rounding Calculator
Round to decimal places or significant figures, in five rounding modes.
Rounded result
How to Use the Rounding Calculator
Enter the number, choose decimal places or significant figures, set how many, pick the rounding rule, and calculate. The exact decision digit is highlighted in the working.
Type the number exactly as written (string-safe, no float artifacts).
Choose decimal places (digits after the point) or significant figures (meaningful digits).
Pick the rule: half up, bankers, floor, ceiling, or truncate. Compare modes on .5 cases.
Decimal Places vs Significant Figures
Use decimal places for money and fixed-format reporting: $19.99, 98.6Β°F. Use significant figures for measured quantities where precision is limited by the instrument: a ruler marked in millimeters justifies 3 sig figs, not 6. Converting: 0.004567 to 2 sig figs is 0.0046 (leading zeros never count); 456700 to 3 sig figs is 457,000. The calculator handles the leading-zero and trailing-zero logic for you.
The Five Rounding Rules
Half up: the school rule; .5 always rounds away from the kept digit upward (2.5 β 3). Half to even (bankers): .5 goes to the even neighbor (2.5 β 2, 3.5 β 4), eliminating systematic bias in bulk statistics and finance. Floor: always toward negative infinity (2.9 β 2, β2.1 β β3). Ceiling: always toward positive infinity (2.1 β 3, β2.9 β β2). Truncate: chop toward zero (2.9 β 2, β2.9 β β2). Floor and truncate differ only on negatives; the comparison table above shows it.
Rounding in Real Life
Cash transactions in countries without 1-cent coins round to the nearest 5 cents (Swedish rounding: a variant of half up). Tax computations often specify the exact rule by law. Grade boundaries usually truncate or use half up, never bankers. Spreadsheets: Excel's ROUND is half up (away from zero on .5 for positives), while Python's round() is bankers, a classic source of "but Excel says" confusion. When precision matters, name the rule explicitly instead of assuming.
Frequently Asked Questions
What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point: 3.14159 to 2 decimal places is 3.14. Significant figures count meaningful digits from the first nonzero digit: 3.14159 to 3 significant figures is 3.14, but 0.00314159 to 3 sig figs is 0.00314. Science uses sig figs because they track measurement precision; money uses decimal places.
What is bankers rounding?
Bankers rounding (round half to even) sends .5 to the nearest even digit: 2.5 β 2, 3.5 β 4. Over thousands of operations it avoids the upward bias of always rounding .5 up, which is why it is the default in IEEE floating point, Python's round(), and financial systems. Select it above to compare.
When should I use floor or ceiling?
Floor (round down) when you need a guaranteed lower bound: how many full boxes fit, complete weeks in a schedule. Ceiling (round up) when partial units still cost a whole one: paint cans, bus seats, server capacity. Money math almost always wants explicit floor/ceiling rather than nearest.
Why does 2.675 round to 2.67 in some tools?
Floating-point representation: 2.675 cannot be stored exactly in binary, so it is actually 2.67499999... and rounds down. It is a storage artifact, not a math error. This calculator uses decimal-safe rounding on the string you type, so 2.675 rounds to 2.68 as you expect.
How many significant figures should I keep?
Match your least precise input. Multiplying 12.5 (3 sig figs) by 3.2 (2 sig figs) gives a result meaningful to 2 sig figs: 40, not 40.0. Keeping extra digits implies precision you do not have; dropping too many throws away real information.