Learn round-half-to-even and why it matters in finance and statistics
Bankers' rounding (also called "round half to even" or "unbiased rounding") is a rounding method that eliminates statistical bias. When a number is exactly halfway between two values (ends in .5), it rounds to the nearest even number.
If exactly .5:
Round to the nearest EVEN number
If not .5:
Use standard rounding (5+ up, <5 down)
| Number | Bankers' Rounding | Standard Rounding | Explanation |
|---|---|---|---|
| 2.5 | 2 | 3 | Rounds to even (2) |
| 3.5 | 4 | 4 | Rounds to even (4) |
| 4.5 | 4 | 5 | Rounds to even (4) |
| 5.5 | 6 | 6 | Rounds to even (6) |
| 3.4 | 3 | 3 | Not .5, rounds down |
| 3.6 | 4 | 4 | Not .5, rounds up |
💡 Notice: Sometimes it rounds up (3.5→4, 5.5→6), sometimes down (2.5→2, 4.5→4). This eliminates bias over many calculations!
Standard rounding always rounds .5 UP, creating an upward bias over many calculations.
Example: If you round 2.5, 3.5, 4.5, and 5.5 using standard rounding, you get 3+4+5+6=18. With bankers' rounding, you get 2+4+4+6=16 (closer to the true average of 15.5).
Banks and financial institutions use this to prevent systematic rounding errors from accumulating.
Over millions of transactions, always rounding .5 up would create significant imbalances.
IEEE 754 floating-point standard (used by most computers) specifies round-to-even as the default.
round() functionMath.Round()Math.rint()round(2.5) # 2 (rounds to even)
round(3.5) # 4 (rounds to even)
Math.Round(2.5, MidpointRounding.ToEven); // 2
Math.Round(3.5, MidpointRounding.ToEven); // 4
=MROUND(2.5, 1) // Uses bankers' rounding
Note: Excel's ROUND function uses standard rounding, not bankers'
✓ Pros:
✗ Cons:
✓ Pros:
✗ Cons:
When exactly .5:
Round to nearest EVEN number
2.5 → 2 (even)
3.5 → 4 (even)
4.5 → 4 (even)
Eliminate statistical bias
Banking, statistics, Python, IEEE 754