What is rounding?
Rounding replaces a number with a nearby value that has fewer digits (easier to read, report, or compute with).
Rounding is used when you want a cleaner number: for reporting, invoicing, percentages, or standardizing precision in calculations.
The key is to define two things: what you're rounding to (whole number, 2 decimals, 3 significant figures, etc.) and which rule you use for ties (like 2.5).
- 1.234 rounded to 2 decimals → 1.23
- 1.235 rounded to 2 decimals (half up) → 1.24
Try it: Decimal places
Precision target + rounding rule = consistent results.
Rounding to decimal places
Decimal-place rounding keeps a fixed number of digits after the decimal point.
This is common in prices, rates, and measurement outputs. For example, currency often uses 2 decimal places, while rates may use 2–4.
A decimal-safe calculator avoids common floating-point pitfalls (for example, 1.005 to 2 decimals should be 1.01).
- 1.005 rounded to 2 decimals → 1.01
- 99.999 rounded to 1 decimal → 100.0
Try it: Decimal places
Decimal-place rounding is about a fixed number of digits after the decimal.
Rounding to significant figures
Significant figures preserve meaningful digits relative to the number's magnitude.
Significant-figure rounding is useful in science, statistics, and summary reporting. It keeps the same number of meaningful digits whether the value is large or small.
Example: 1,234 rounded to 2 significant figures becomes 1,200. But 0.01234 rounded to 2 significant figures becomes 0.012.
- 1234 → 2 sig figs → 1200
- 0.01234 → 2 sig figs → 0.012
Try it: Significant figures
Significant figures adapt the rounding step based on magnitude.
Rounding modes (half-up, half-even, etc.)
Different tie-breaking rules exist for “.5” cases — and they matter in finance and statistics.
Half-up is the common “schoolbook” rule: 2.5 → 3. Half-even (banker's rounding) reduces systematic bias in large datasets by rounding ties to the nearest even: 2.5 → 2, 3.5 → 4.
Ceiling, floor, and truncate are directional rules (useful for constraints, tax rules, and programming).
- Half up: 2.5 → 3
- Half even: 2.5 → 2; 3.5 → 4
- Truncate: -2.9 → -2
Try it: Rounding modes
Pick a rounding mode that matches your domain rule and stick to it.
Custom rounding base (nearest X)
Sometimes you need to round to the nearest multiple of X (like 0.05, 5, or 10).
This shows up in currency cash rounding, invoice rounding, retail pricing, and tax rules. The idea is simple: round the number to the nearest multiple of your chosen base.
Example: rounding to the nearest 0.05 makes prices land on 0.00, 0.05, 0.10, 0.15, and so on.
- 1.13 rounded to nearest 0.05 → 1.15
- 18 rounded to nearest 5 → 20
Try it: Custom base
Custom base rounding is rounding to a step size you choose.
FAQs
Why does 1.005 rounded to 2 decimals sometimes show 1.00 in JavaScript?▼
Because many decimals cannot be represented exactly in binary floating point. A decimal-safe approach (like Big.js) performs rounding in base-10 to avoid these errors.
What's the difference between floor and truncate for negative numbers?▼
Truncate moves toward 0 (−2.9 → −2), while floor moves toward −∞ (−2.1 → −3). They match for positive numbers, but differ for negatives.
When should I use half-even (banker's rounding)?▼
Half-even is common in statistics and some accounting contexts because it reduces rounding bias when you round many values with ties.
Can I round to a base like 0.05?▼
Yes. Custom base rounding rounds to the nearest multiple of the base (e.g., 0.05). Make sure the calculator uses decimal-safe math to avoid float issues.