Rounding Calculator — round to decimal places (nearest, up, down)

How it works

Rounding replaces a number with a nearby one that has fewer decimal places. You choose how many places to keep and how to break ties:

• Nearest — round to the closest value. When the digit dropped is exactly a half, this rounds to the even neighbour (2.5 → 2, 3.5 → 4). That's "banker's rounding", used to avoid a systematic upward bias when many numbers are rounded.
• Up (ceiling) — always toward +∞, so 2.1 and 2.9 both become 3.
• Down (floor) — always toward −∞, so 2.1 and 2.9 both become 2.

To round to n decimal places, the same idea is applied after shifting the decimal point n places: round 3.14159 to 2 places by rounding 314.159 to a whole number (314) and shifting back (3.14).

Worked example

Round π = 3.14159 to 2 places (nearest): the third decimal is 1, below a half, so it rounds down to 3.14. Rounding 2.5 to a whole number (nearest) is a tie — the halves rule sends it to the even neighbour, 2 (not 3). And 19.994 rounded up to 2 places becomes 20.00, since "up" always climbs.

Frequently asked questions

What does "round half to even" mean?

When the part being dropped is exactly a half, round to whichever neighbour is even. So 0.5 → 0, 1.5 → 2, 2.5 → 2, 3.5 → 4. Also called banker's rounding, it keeps a long series of roundings from drifting upward the way "always round halves up" does. It's the default here and the convention most computing standards use.

How is that different from "always round 0.5 up"?

The school rule sends every half up (2.5 → 3, 3.5 → 4), which nudges sums slightly high over many values. Round-half-to-even sends halves to the nearest even digit instead, so the up-and-down roundings balance out. The two agree on every value except exact halves.

What do "up" and "down" do to negative numbers?

They follow the number line, not the distance from zero. **Up** (ceiling) goes toward +∞, so −2.7 rounds up to −2. **Down** (floor) goes toward −∞, so −2.1 rounds down to −3. If you want "away from zero" or "toward zero", pick the mode by direction on the number line.

Why did rounding 2.675 to 2 places give 2.67, not 2.68?

Because computers store decimals in binary, and 2.675 can't be represented exactly — it's held as 2.67499999…, which is just below the halfway point, so it rounds down. This is a limitation of floating-point arithmetic, not a mistake in the rule; it affects a small set of "exact half" decimals.

How do I round to the nearest 10, 100 or 5?

For nearest 10 or 100, use a negative number of places conceptually — divide by 10 (or 100), round to a whole number, then multiply back. For "nearest 5", divide by 5, round, and multiply by 5. This calculator rounds to decimal places; scale the input first for those step sizes.

What's the difference between rounding and significant figures?

Rounding keeps a fixed number of **decimal places** (digits after the point); significant figures keep a fixed number of **meaningful digits** counting from the first non-zero one. 0.04052 to 2 decimal places is 0.04, but to 2 significant figures it's 0.041 — different questions, different tools.