Rounding Calculator — Round to Decimal Places, Sig Figs & Banker's Rounding
Round any number to decimal places or significant figures. Covers standard rounding rules, the round half up vs. banker's rounding debate, and where each method is used.
Rounding seems trivial until you're writing financial software and discover that "round 2.5 to the nearest integer" has more than one correct answer — depending on who's asking. Understanding the different rounding methods matters more than most people realize. Round any number exactly the way you need with the CalcHub Rounding Calculator.
Standard Rounding Rules (Round Half Up)
The most familiar method: if the digit to be dropped is less than 5, round down; if 5 or more, round up.
Round 3.456 to 2 decimal places: Look at the 3rd decimal: 6 ≥ 5, so round up. 3.46 Round 7.834 to 1 decimal place: Look at the 2nd decimal: 3 < 5, so round down. 7.8 Round 142.5 to the nearest integer: Look at the decimal: 5 ≥ 5, so round up. 143Rounding to Decimal Places
| Original | To 0 dp | To 1 dp | To 2 dp | To 3 dp |
|---|---|---|---|---|
| 3.14159 | 3 | 3.1 | 3.14 | 3.142 |
| 0.00546 | 0 | 0.0 | 0.01 | 0.005 |
| 123.456 | 123 | 123.5 | 123.46 | 123.456 |
| 9.9999 | 10 | 10.0 | 10.00 | 10.000 |
Banker's Rounding (Round Half to Even)
Standard "round half up" introduces a systematic bias: when you round many .5 values, they all go up. Over millions of financial transactions, this adds up to real money.
Banker's rounding (also called "round half to even" or "statistician's rounding") breaks ties by rounding to the nearest even digit:| Number | Round Half Up | Banker's Rounding |
|---|---|---|
| 0.5 | 1 | 0 (nearest even) |
| 1.5 | 2 | 2 (nearest even) |
| 2.5 | 3 | 2 (nearest even) |
| 3.5 | 4 | 4 (nearest even) |
| 4.5 | 5 | 4 (nearest even) |
| 5.5 | 6 | 6 (nearest even) |
Other Rounding Methods
| Method | Rule | Use Case |
|---|---|---|
| Round half up | .5 → round up | General math, everyday use |
| Round half down | .5 → round down | Some statistical applications |
| Round half to even | .5 → nearest even | Finance, IEEE 754, Python |
| Round half to odd | .5 → nearest odd | Rare, specialized |
| Round half away from zero | .5 → away from 0 | Tax calculations |
| Truncation (floor) | Always drop digits | Clock displays, integer division |
| Ceiling | Always round up | Number of buses needed |
Rounding in Different Contexts
Money: Tax calculations often use "round half away from zero" to avoid giving/losing fractions of a cent. $0.005 rounds to $0.01, not $0.00. School grades: Most teachers use "round half up" — 89.5% becomes 90%. Statistics: Banker's rounding is preferred to avoid accumulation of rounding errors. Programming: Know your language's default! Python 3 uses banker's rounding. Java'sMath.round() uses round half up. JavaScript's Math.round() uses round half up.
Engineering: Round to significant figures rather than decimal places — see the Significant Figures Calculator.
Rounding Errors in Computation
Repeated rounding of intermediate results accumulates error. For example, rounding at each step of a long calculation:
Exact: 1/3 + 1/3 + 1/3 = 1.000
With 2dp rounding: 0.33 + 0.33 + 0.33 = 0.99
Best practice: carry full precision through calculations, round only the final result.
Why does rounding 2.5 sometimes give 2 in Python?
Python 3 uses banker's rounding (round half to even). round(2.5) = 2 because 2 is the nearest even integer. round(3.5) = 4 for the same reason. If you need "round half up" behavior in Python: import math; math.floor(x + 0.5) or use the decimal module with ROUND_HALF_UP.
How does rounding affect the final digit in long division?
When you divide and get a repeating decimal, rounding the last digit can depend on the method used. For critical financial calculations, always specify which rounding rule applies — "round half up," "truncate," etc. — in your documentation or specifications to avoid ambiguity.
When should you round intermediate calculations?
Ideally, never — carry full precision and round only the final answer. Each intermediate rounding introduces small errors that compound. This is especially important in physics calculations, financial models, and any iterative process where outputs feed back as inputs.