Rounding Calculator

📋

Walk-through

How to Use This Calculator

3 steps

1

Enter the number to round

Type any real number into the field — positive, negative, whole, or decimal (for example 2.5, 1234, or -0.0875). The result updates instantly as you type.

2

Choose what to round to

Pick a place value or nearest multiple, a number of decimal places, or a count of significant figures. Each target controls how precise the rounded answer will be.

3

Pick a rounding mode and read the result

Select a mode — half up, half down, banker's (half to even), ceiling, floor, truncate, or away from zero. The result shows the before to after value, the deciding digit, and which rule applied. Open the Modes Explained tab to compare every mode side by side.

⚡

Reference

Formula & Methodology

4 formulas

Core: round to the nearest multiple

rounded = applyMode(value / m) x m

Every target reduces to one step m. Divide the value by m to get a quotient, round that quotient to an integer using the chosen mode, then multiply back by m. For nearest-10 use m = 10; for nearest-hundredth use m = 0.01.

Decimal places to a multiple

m = 10^(-d) (d = number of decimal places)

Rounding to d decimal places is the same as rounding to the nearest 10^-d. Two decimals means m = 0.01; zero decimals means m = 1 (nearest integer).

Significant figures to a multiple

m = 10^(floor(log10(|value|)) - s + 1)

Nearest modes agree away from exact ties. Directed modes can disagree on any nonintegral step: floor, ceiling, truncation and rounding away from zero use different directions. The highlighted rows identify exact ties; compare every row for the actual mode results.

Tie-breaking on an exact half

half-up: 0.5 -> +inf | half-down: 0.5 -> -inf | half-even: 0.5 -> nearest even

Modes only disagree when the fraction is exactly one half. Half up sends ties toward positive infinity, half down toward negative infinity, and banker's rounding sends them to the nearest even integer to cancel long-run bias.

📖

Glossary

Key Terms Explained

7 terms

Rounding mode The rule that decides how a number is shortened — especially how an exact halfway value (a tie) is resolved. This calculator supports seven distinct modes.

Banker's rounding (half to even) A nearest-value rule that chooses the even step at an exact tie. Nearest rules agree away from ties; directed rules such as floor or ceiling may still differ.

Significant figures The digits in a number that carry real precision, counted from the first non-zero digit. 0.00346 and 1230 both have three significant figures; trailing zeros before a decimal are ambiguous.

Decimal places The count of digits kept to the right of the decimal point. Rounding 3.14159 to two decimal places gives 3.14, regardless of the size of the whole-number part.

Place value The value a digit represents based on its position — thousands, hundreds, tens, ones, tenths, hundredths. Rounding to a place value snaps the number to the nearest such multiple.

Tie / exact half A value exactly halfway between adjacent rounding steps. Highlighted rows mark ties; directed rules can also differ away from ties, so compare every row.

Rounding bias A systematic drift introduced when many numbers are rounded the same way. Always rounding halves up inflates totals; banker's rounding keeps the long-run sum closer to the true value.

👥

Scenarios

Real-World Examples

3 worked examples

🏦

Banker's vs half-up

Round 2.5 to a whole number

Number 2.5 Round to 0 decimal places Mode half-even vs half-up

2.5 is an exact halfway value. Banker's rounding (half to even) gives 2 because 2 is even, while round half up gives 3. This single case is why two correct calculators can disagree — the mode, not the math, is the difference.

📐

Fixed decimals

Round 3.14159 to 2 decimal places

Number 3.14159 Round to 2 decimal places Mode half up

The deciding digit is the third decimal, 1, which is below 5, so the value rounds down to 3.14. Decimal-place rounding ignores the size of the whole number — only the digits past the cut-off matter.

🔬

Significant figures

Round 0.0034567 to 3 significant figures

Number 0.0034567 Round to 3 significant figures Mode half up

Leading zeros are not significant, so the first three figures are 3, 4, and 5. The next digit is 6, which rounds the 5 up, giving 0.00346. Significant figures track precision, which is why scientists prefer them over a fixed decimal count.

🔗

Reference

Cite This Calculator

APA & MLA

Use either format to cite this calculator in a paper, report, or resource list.

APA

MLA

📄

Deep Dive

Understanding the Rounding Calculator

4 chapters · 4 min read

Rounding looks trivial until two tools give you different answers for 2.5. The reason is almost never a bug — it is the rounding mode. This calculator exposes every common mode, lets you round by place value, decimal places, or significant figures, and shows all modes side by side so you can see exactly where they diverge.

Why 2.5 rounds differently

An exact half is the only case where rounding rules disagree. Round half up pushes 2.5 to 3; round half down pushes it to 2; banker's rounding (round half to even) sends it to 2 because 2 is even, but rounds 3.5 to 4. For any value that is not exactly halfway, every mode that rounds to the nearest integer agrees. That is why most numbers behave identically everywhere and only the halves cause arguments.

Banker's rounding and bias

Nearest modes agree away from exact ties. Directed modes can disagree on any nonintegral step: floor, ceiling, truncation and rounding away from zero use different directions. The highlighted rows identify exact ties; compare every row for the actual mode results.

Significant figures vs decimal places

Decimal places count digits to the right of the point, regardless of the number's size: 3.14159 to two decimals is 3.14, and 12345.678 to two decimals is 12,345.68. Significant figures count meaningful digits from the first non-zero digit, so they track precision across magnitudes: 0.0034567 to three sig figs is 0.00346, and 12,345 to three sig figs is 12,300. Use decimal places for money and fixed-format reports; use significant figures for scientific measurements where the magnitude varies.

Negatives and directed rounding

Negative numbers expose the difference between directed modes. Ceiling always moves toward positive infinity, so -2.7 becomes -2; floor moves toward negative infinity, so -2.3 becomes -3. Truncate (toward zero) drops the fraction, turning -2.9 into -2, while away from zero turns -2.1 into -3. JavaScript's built-in rounding helpers are biased for negatives — Math.round turns -2.5 into -2 (toward +infinity) — which is exactly why this calculator implements each mode explicitly instead of relying on them.

❓

Questions

Frequently Asked Questions

6 questions

Why does my calculator round 2.5 down to 2?+

It is using banker's rounding (round half to even), the default in IEEE 754 floating point and most spreadsheets. On an exact half it rounds to the nearest even number, so 2.5 goes to 2 but 3.5 goes to 4. Switch the mode to round half up to get the schoolbook answer of 3.

What is banker's rounding and when should I use it?+

Banker's rounding sends exact halves to the nearest even number instead of always up. Across many values the up-and-down ties cancel, so totals stay unbiased. Use it for financial summaries, accounting, and statistics where rounding the same direction every time would inflate the result.

What is the difference between significant figures and decimal places?+

Decimal places count digits after the point no matter the number's size. Significant figures count meaningful digits from the first non-zero digit, so they preserve precision across magnitudes. 0.0034567 to three significant figures is 0.00346, but to three decimal places it is 0.003.

How are negative numbers rounded?+

Each mode is applied by its true definition. Ceiling rounds toward positive infinity (-2.7 to -2), floor toward negative infinity (-2.3 to -3), truncate toward zero (-2.9 to -2), and away from zero pushes -2.1 to -3. Half-up sends -2.5 to -2, while away from zero sends it to -3.

Can the result be off by a tiny amount because of floating point?+

Computers store decimals like 1.005 in binary, where the stored value is fractionally below the exact one, which can make a naive rounding drop the wrong way. This calculator cleans that floating-point dust before deciding, so exact halves and values like 1.005 round the way you expect.

Can I share or export my results?+

Yes. The Share button copies a link that encodes your number, target, and mode, so a colleague opens the exact same calculation. The CSV button downloads a table of all seven modes for your current input, which is handy for documenting why a value rounds the way it does.

Download a one-page PDF of your numbers instantly. Add your email to also get our occasional calculator tips — no spam, unsubscribe anytime. Privacy.

Related calculators

Guides & articles

Glossary terms

Calculator topicRounding

Inputs

Result

All modes, same input

How to Use This Calculator

Enter the number to round

Choose what to round to

Pick a rounding mode and read the result

Formula & Methodology

Key Terms Explained

Real-World Examples

Banker's vs half-up

Fixed decimals

Significant figures

Cite This Calculator

Understanding the Rounding Calculator

Why 2.5 rounds differently

Banker's rounding and bias

Significant figures vs decimal places

Negatives and directed rounding

Frequently Asked Questions

Get a branded PDF of your results

Rounding Calculator

Inputs

Result

All modes, same input

How to Use This Calculator

Enter the number to round

Choose what to round to

Pick a rounding mode and read the result

Formula & Methodology

Key Terms Explained

Real-World Examples

Cite This Calculator

Understanding the Rounding Calculator

Why 2.5 rounds differently

Banker's rounding and bias

Significant figures vs decimal places

Negatives and directed rounding

Frequently Asked Questions

Get a branded PDF of your results

Keep Exploring

Related calculators

Guides & articles

Glossary terms