Rounding Calculator

Round numbers to decimal places, significant figures, or nearest integer. Choose from multiple rounding methods including banker's rounding.

Formula:Round(x, n) = floor(x × 10ⁿ + 0.5) / 10ⁿ

Rounding Result

Rounded Value

3.14

2 decimal places

Original3.14159265
Rounded3.14
Difference-0.0015926500
% Error0.050696%

Number to Round

Rounding Options

Formula Used

round(3.14159265 × 10^2) / 10^2

Quick Reference

Decimal PlacesRounded Value
0 places3
1 places3.1
2 places3.14
3 places3.142
4 places3.1416
5 places3.14159

Method Comparison

MethodResult
standard3.14
half even3.14
up3.15
down3.14
truncate3.14

Common Examples

2.5 with different methods:

  • Standard: 3
  • Banker's: 2
  • Ceiling: 3
  • Floor: 2

3.5 with different methods:

  • Standard: 4
  • Banker's: 4
  • Ceiling: 4
  • Floor: 3

Rounding Result

Rounded Value

3.14

2 decimal places

Original3.14159265
Rounded3.14
Difference-0.0015926500
% Error0.050696%

?How Do You Round Numbers?

Rounding simplifies numbers to a specified precision. Standard rounding: digits 5-9 round up, 0-4 round down. For 3.567 to one decimal: 3.6 (7 rounds up). Round to nearest 10: 3,567 becomes 3,570. Significant figures count from the first non-zero digit. Always consider the digit after your rounding position.

What is Rounding?

Rounding is the process of replacing a number with an approximation that has fewer significant digits. It simplifies numbers for easier communication, calculation, or representation while maintaining reasonable accuracy. Different rounding rules (standard, ceiling, floor, banker's) serve different purposes in mathematics, science, and finance.

Key Facts About Rounding

  • Standard rounding: 0-4 round down, 5-9 round up
  • Round to decimal places: specify digits after decimal point
  • Significant figures: count from first non-zero digit
  • Round up (ceiling): always round away from zero
  • Round down (floor): always round toward zero
  • Banker's rounding: 5 rounds to nearest even (reduces bias)
  • Rounding affects precision vs. accuracy in measurements
  • Scientific notation rounding maintains significant figures

Quick Answer

Rounding simplifies numbers to a specified precision. Standard rounding: digits 5-9 round up, 0-4 round down. For 3.567 to one decimal: 3.6 (7 rounds up). Round to nearest 10: 3,567 becomes 3,570. Significant figures count from the first non-zero digit. Always consider the digit after your rounding position.

Frequently Asked Questions

Standard/Half-Up: rounds 0.5 up. Half-Even (Banker's): rounds 0.5 to nearest even number, reduces bias. Round Up (Ceiling): always rounds up. Round Down (Floor): always rounds down. Truncate: removes decimal places without rounding.
Banker's rounding (half-even) rounds 0.5 to the nearest even number. So 2.5 rounds to 2, but 3.5 rounds to 4. This reduces cumulative rounding bias in financial calculations where you round many numbers.
Significant figures are the meaningful digits in a number. Leading zeros are not significant. For example, 0.00456 has 3 sig figs. Trailing zeros after decimal are significant (4.50 = 3 sig figs). Used in science to show measurement precision.
Divide by the rounding unit, round to nearest integer, then multiply back. Example: 1234 to nearest 100 = round(1234/100) × 100 = round(12.34) × 100 = 12 × 100 = 1200.
Floating-point numbers can't represent all decimals exactly. 0.1 + 0.2 = 0.30000000000000004 in most languages. Use integer cents for money, libraries like decimal.js for precision, or round only at final display.

Last updated: 2025-01-15