Rounding Calculator
Round any number to decimal places, significant figures, place value, fractions, or currency. 5 rounding methods including standard, banker's, ceiling, and floor. Free, instant results.
Enter a number to round
Supports decimal places, sig figs, place value, fractions, and currency
Rounding Quick Reference Chart
Common rounding examples using standard (half up) method.
How to Use the Rounding Calculator
Enter Your Number
Type any number including decimals, negative numbers, and large values. Use the preset buttons for common examples or type your own value. The calculator handles integers, decimals, and very small or large numbers.
Choose What to Round To
Select decimal places (0-8), significant figures (1-8), place value (ones through millions), nearest fraction (1/2 through 1/64), or currency rounding (cent, dollar, $5, $10, $100). Each mode shows appropriate options.
Select Rounding Method
Standard (half up) is the default and most common. Banker's rounding rounds 5 to even numbers. Ceiling always rounds up, floor always rounds down. See all 5 methods compared side by side in the results panel.
Why Use Our Rounding Calculator
5 Rounding Methods
Standard, half down, banker's (half even), ceiling, and floor. Compare results across all methods simultaneously.
5 Target Types
Round to decimal places, significant figures, place value, fractions, or currency denominations. Every rounding scenario covered.
Currency Rounding
Round to nearest cent, dollar, $5, $10, or $100. Perfect for tax calculations, pricing, and financial reports.
Full Comparison View
See your number rounded to nearest whole, tenth, hundredth, ten, hundred, and thousand all at once.
Instant Real-Time Results
Results update as you type. No buttons to click, no loading. Change any setting and see the impact immediately.
Precise and Private
Handles numbers of any size with floating-point precision. All calculations in your browser - no data sent anywhere.
Complete Guide to Rounding Numbers
How Rounding Works: The Basic Rules
Rounding replaces a number with a simpler, approximate value. The standard rule taught in schools is: look at the digit immediately after your rounding position. If it is 5 or greater, round up. If it is 4 or less, round down. For example, rounding 3.456 to the nearest tenth: the digit after the tenths place is 5, so round up from 3.4 to 3.5.
This standard method is called "round half up" because when the deciding digit is exactly 5, the number rounds up. It is the most commonly used method worldwide and the one taught in most math courses. However, it introduces a slight upward bias when applied to large datasets because 5 always goes up, never down.
Rounding to Decimal Places vs Significant Figures
Decimal places count positions after the decimal point. Rounding 3.14159 to 2 decimal places gives 3.14. Significant figures count all meaningful digits from the first non-zero digit. Rounding 0.004567 to 3 significant figures gives 0.00457 - the leading zeros are not significant.
Significant figures are preferred in scientific measurements because they communicate the precision of the measurement. A measurement of 1200 could mean exactly 1200 (4 sig figs) or approximately 1200 (2 sig figs). Writing 1.2 x 10^3 makes it clear there are 2 significant figures. In engineering and chemistry, sig figs prevent you from claiming more precision than your instruments can measure.
Banker's Rounding: Why 2.5 Rounds to 2
Banker's rounding (IEEE 754 default, also called round half to even) rounds 5 to the nearest even number. So 2.5 becomes 2, 3.5 becomes 4, 4.5 becomes 4, and 5.5 becomes 6. This eliminates the upward bias of standard rounding because half the time 5 goes up, half the time it goes down.
Financial institutions, statistical software (R, Python numpy), and database systems use banker's rounding by default. When processing millions of transactions, the bias from always rounding 5 up can create material discrepancies. A bank processing 10 million transactions rounded with standard rules would show a systematic overcount. Banker's rounding solves this by ensuring statistical neutrality.
Ceiling and Floor: When Direction Matters
Ceiling (round up) always goes toward positive infinity. Floor (round down) always goes toward negative infinity. These are not the same as rounding away from or toward zero for negative numbers. Ceiling of -2.3 is -2 (toward positive infinity). Floor of -2.3 is -3 (toward negative infinity).
Ceiling is used when you need "at least" something: if a project needs 2.3 gallons of paint, ceiling tells you to buy 3 gallons. Floor is used for "at most" scenarios and for truncation. Integer division in most programming languages uses floor division (7/2 = 3, not 4). Understanding the difference prevents off-by-one errors in code and real-world calculations.
Rounding in Money and Currency Calculations
Most currencies round to the nearest cent (0.01). Tax calculations often round each line item independently, which can produce different totals than rounding the sum. For example, three items at $1.005 each round to $1.01 each (total $3.03), but the unrounded total $3.015 rounds to $3.02. This one-cent difference matters in accounting.
Some countries have eliminated small coins. Canada rounds cash transactions to the nearest 5 cents. Australia and New Zealand round to the nearest 5 or 10 cents. Sweden rounds to the nearest krona. In these countries, electronic payments use exact amounts but cash transactions are rounded. Our currency rounding mode handles all these scenarios.
Rounding in Programming: Common Pitfalls
Floating-point numbers in computers cannot exactly represent most decimals. The classic example: 0.1 + 0.2 = 0.30000000000000004 in JavaScript. This means rounding 2.55 to 1 decimal place might give 2.5 instead of 2.6 because 2.55 is stored as 2.54999999... The solution is to multiply by the appropriate power of 10, round the integer, then divide back.
Different languages handle rounding differently. JavaScript Math.round() uses standard rounding. Python round() uses banker's rounding by default. Java has BigDecimal with configurable rounding modes. SQL databases vary: MySQL uses standard rounding, PostgreSQL uses banker's rounding. Always test your rounding behavior and document which method your application uses.
Rounding Calculator FAQ
Common questions about rounding numbers, methods, and decimal places.
Disclaimer: This Rounding Calculator handles standard IEEE 754 floating-point arithmetic. Very large or very small numbers may have precision limitations inherent to floating-point representation. For financial calculations requiring exact decimal arithmetic, verify results with dedicated financial software.