Math calculator

Free rounding calculator

Round any number to a specified decimal place or significant figure — enter a value and choose how to round, updated live, as you type.

On this page10 sections

InputsLive

Rounding mode

Value

Any decimal number (positive or negative).

Decimal places

Integer from 0 to 10.

Result

Rounded value

3.14

3.14159 rounded to 2 dp (Nearest (banker's)) = 3.14

Original value3.14159

Rounded result3.14

Decimal places2

Rounding modeNearest (banker's)

“Nearest” uses banker's rounding (round half to even). “Up” = ceiling (towards +∞), “Down” = floor (towards −∞). “Truncate” drops digits towards zero.

Results are estimates. Consult a professional.

How it's calculated

How the rounding calculator works

Rounding replaces a number with a nearby value that is simpler or more appropriate for a given precision. Two common modes are decimal places (how many digits after the decimal point) and significant figures (how many non-zero leading digits are kept). The standard rule is 'round half up': if the digit immediately after the cutoff is 5 or more, increment the last kept digit.

Round to d decimal places: look at digit d+1; if ≥ 5 add 1 to digit d

Round to s significant figures: find the sth non-zero digit, then apply same half-up rule

Truncate: discard all digits past the cutoff (no rounding up)

Weisstein, E. W. Rounding. MathWorld.

Example

Worked example: rounding 3.7462

Example: 3.7462 rounded to different precisions

Starting with 3.7462, we apply rounding to 2 decimal places, 3 significant figures, and the nearest integer. The digit after each cutoff determines whether we round up or keep the value.

To 2 decimal places: 3.74|62 → digit after = 6 ≥ 5 → 3.75

To 3 significant figures: 3.74|62 → digit after = 6 ≥ 5 → 3.75

To nearest integer: 3.|7462 → digit after = 7 ≥ 5 → 4

0.00456 to 2 sig figs: 0.0045|6 → digit after = 6 ≥ 5 → 0.0046

3.75

3.7462 rounded to 2 decimal places (or 3 significant figures) is 3.75.

Quick reference

Rounding examples at various precisions

The table below shows how the same number looks at different levels of rounding precision.

Original	2 decimal places	3 sig figs	Nearest integer
3.7462	3.75	3.75	4
0.08951	0.09	0.0895	0
123.456	123.46	123	123
9.9999	10.00	10.0	10
0.00456	0.00	0.00456	0
−7.315	−7.32	−7.32	−7

All examples use round-half-up. Negative numbers round toward zero for half-up.

Practical tips

Tips for rounding numbers

Choosing the right rounding method and precision avoids misleading results.

Match precision to context — money typically rounds to 2 decimal places, measurements to 3–4 significant figures, population counts to the nearest thousand.
Don't round intermediate steps — carry full precision through a multi-step calculation and round only the final answer to avoid accumulated rounding error.
Know the difference between decimal places and sig figs — 0.00456 rounded to 2 decimal places is 0.00 (a meaningless result); 2 significant figures gives 0.0046.
Be aware of banker's rounding — some software rounds 0.5 to the nearest even number (e.g. 2.5 → 2, 3.5 → 4) to reduce statistical bias; check which rule applies.
Use rounding to check estimates — round each input to 1 significant figure for a quick mental sanity check before trusting a calculator result.

Accuracy & limits

Accuracy and limitations

The calculator uses round-half-up as the default convention. Some applications require round-half-even (banker's rounding) or round-half-down — check your discipline's standards. Floating-point representation means that some decimals (e.g. 0.1, 0.2) cannot be stored exactly in binary, which can produce unexpected results like 0.1+0.2 ≠ 0.3 in raw arithmetic. The calculator accounts for this with decimal-safe arithmetic where possible, but very long decimal inputs may still show minor discrepancies.

Glossary

Key terms

The number of digits written to the right of the decimal point in a rounded result.

The count of meaningful digits in a number, starting from the first non-zero digit.

The rule that a digit of exactly 5 causes the preceding digit to be incremented — the most common everyday convention.

Rounds 0.5 to the nearest even digit to reduce long-run statistical bias (also called round-half-even).

Dropping all digits past a given position without rounding up, always rounding toward zero.

The difference between a rounded value and the exact value; accumulates when intermediate results are rounded.

About

About this calculator

Part of our math calculators suite — explore all calculators.

Questions

Frequently asked questions about the free rounding calculator

A rounding calculator is a free online tool that helps you round any number to any precision — nearest (banker's), ceiling, floor, or truncate. Rounding reduces a number's precision to a chosen number of decimal places. Different modes serve different purposes — banker's rounding for accounting, ceiling for upper bounds, floor for lower bounds. It runs entirely in your browser with instant results and no sign-up.

When the value falls exactly on the rounding boundary (e.g. 2.5 to a whole number), banker's rounding rounds to the nearest EVEN integer instead of always rounding up. So 2.5 → 2, but 3.5 → 4. This eliminates the small upward bias that 'round half up' introduces when summing many rounded values. It's the IEEE 754 default and used by most accounting and statistical systems.

For positive numbers, they're the same: 3.99 truncated or floored gives 3. For negative numbers, they differ: −3.99 truncated gives −3 (toward zero), but floored gives −4 (toward −∞). Truncate is 'cut off the fractional part'; floor is 'always round to the next-smaller integer'.

Nearest (banker's) for most cases — it preserves precision on average. Ceiling when you need an upper bound (max storage to allocate). Floor when you need a lower bound (whole units that fit). Truncate when you're working with signed values and want a consistent 'drop the decimal' behavior.