What is the difference between rounding to nearest, up, and down?

To nearest uses the half-up rule: look at the first dropped digit; 5 or more rounds the kept digit up, 4 or less leaves it. Up (ceiling) always moves to the next value away from zero — 3.14159 to 2 places is 3.15. Down (floor) always moves toward zero — 3.14159 to 2 places is 3.14.

Why did 3.14159 round to 3.14 and not 3.15?

Rounding to 2 decimal places keeps the hundredths digit (4) and checks the next digit, which is 1. Because 1 is less than 5, the kept digit stays put and the rest is dropped: 3.14. Only a decision digit of 5 or more would push it to 3.15.

How do I round to a whole number?

Set decimal places to 0. The calculator then looks at the tenths digit: 3.6 becomes 4 to the nearest, 4 when rounding up, and 3 when rounding down.

Is it safe to round numbers in the middle of a calculation?

Usually not. Rounding intermediate steps lets small errors compound, so keep full precision while you work and round only the final answer — that is the single rounding the steps panel reproduces.

Rounding Calculator

Round any number to any number of decimal places: nearest (half up), up, or down. Compare all three modes side by side on a number line, with exact half-up handling of tricky cases like 2.675. Results update instantly. Free, no sign-up.

Number

Typed as text so digits stay exact.

Decimal places

Rounding mode

Advanced options

Strip trailing zeros (2.50 → 2.5)

Round to significant figures instead

How Rounding Modes Work

Half up (the schoolbook rule): look at the first dropped digit — 5 or more rounds away from zero. Up (ceiling) always moves toward +∞, and down (floor) always toward −∞, regardless of the dropped digit. For positive numbers up and half-up often agree, but they split on negatives: −2.5 rounds to −3 under half-up (away from zero) yet −2 under ceiling.

The classic trap is 2.675 to 2 decimals. In binary floating point 2.675 is stored as 2.67499999…, so naive code returns 2.67. This calculator rounds the typed digits exactly, giving the correct 2.68 — the number line below shows where each mode lands.

Rounding in Real Life

Cash registers round to cents, payroll systems round hours to quarter-hours, and statisticians round to avoid implying false precision. Banker's rounding (half to even) exists to remove bias in large datasets, but everyday math — and this calculator's default — uses half up.

Frequently Asked Questions

Why does 2.675 round to 2.68 and not 2.67?

The dropped digit is 5, and half-up rounds 5s away from zero. (Computers sometimes say 2.67 because 2.675 can't be stored exactly in binary — this calculator uses your typed digits, so it gets 2.68.)

What is the difference between rounding up and half up?

Half up only moves on ties (5+) or higher digits; ceiling moves up for any dropped digit at all. 2.61 → 2.6 half-up, but 2.7 ceiling.

How do negative numbers round?

Half up goes away from zero (−2.5 → −3); ceiling goes toward +∞ (−2.5 → −2); floor goes toward −∞ (−2.5 → −3).

What are significant figures?

Digits that carry meaning, counted from the first non-zero digit. 0.004560 has 4 significant figures; toggle the advanced option to round by sig figs instead of decimal places.

What is banker's rounding?

Ties round to the nearest even digit (2.5 → 2, 3.5 → 4) to avoid upward bias across many values. Not included here — half up is the everyday default.

Rounding Calculator

How Rounding Modes Work

Rounding in Real Life

Frequently Asked Questions

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