Rounding calculator —
decimal places & significant figures.

Field guide

Rounding rules, methods, and when to use each one.

How rounding works: the basic rule

Rounding replaces a number with a simpler approximation at a chosen level of precision. The standard rule (round half up) is:

• Identify the digit at the target precision (the "rounding digit").
• Look at the digit immediately to the right (the "deciding digit").
• If the deciding digit is 5 or greater: add 1 to the rounding digit and drop everything to its right.
• If the deciding digit is 4 or less: keep the rounding digit unchanged and drop everything to its right.

For example: rounding 3.14159 . The rounding digit is 4, the deciding digit is 1 (less than 5), so the result is 3.14.

Decimal places vs significant figures

These two rounding targets are fundamentally different and frequently confused:

• Decimal places count the digits after the decimal point. Rounding 0.00314 to 2 decimal places gives 0.00, both significant digits are lost. This is almost never what you want for very small numbers.
• Significant figures count all non-zero digits (plus zeros between them or trailing zeros after the decimal). Rounding 0.00314 to 2 significant figures gives 0.0031 — preserving the meaningful precision.

Rule of thumb: use decimal places for money and measurements where the absolute precision matters (you always want 2 decimal places for dollars). Use significant figures for scientific quantities where relative precision matters (you want 3 sig figs of a measurement regardless of its magnitude).

The five rounding methods

1. Round half up (standard)

The most common method. When the deciding digit is exactly 5, round away from zero. This is the rule most people learn in school and the default in most spreadsheets and calculators.

2. Banker's rounding (round half to even)

When the deciding digit is exactly 5 and all following digits are zero, round to the nearest even digit. This eliminates the systematic upward bias of half-up rounding — over many rounded values, half round up and half round down, keeping the mean correct. Widely used in financial systems, the IEEE 754 floating-point standard, and Python's built-in round() function.

3. Truncate (round toward zero)

Simply discard all digits beyond the target precision — no rounding up occurs. Also called "round down" or "chop." Useful when you need a safe lower bound (e.g., integer division in programming) or for displaying partial results where an overshoot would be misleading.

4. Floor (round toward −∞)

Always rounds to the largest integer less than or equal to the number. Equivalent to truncation for positive numbers, but rounds away from zero for negative numbers. Used in interval arithmetic and computing daily timestamp "day buckets."

5. Ceiling (round toward +∞)

Always rounds to the smallest integer greater than or equal to the number. Rounds up for positive numbers and toward zero for negative numbers. Used when computing page counts, minimum container sizes, or "at least n" bounds.

Rounding to place values (tens, hundreds, thousands)

Rounding to the nearest ten means that 47 → 50, 43 → 40, and 45 → 50 (half-up). This is equivalent to rounding to −1 decimal places. More generally:

• Nearest 10: multiply by 0.1, round to integer, divide by 0.1
• Nearest 100: multiply by 0.01, round, divide by 0.01
• Nearest 1,000: multiply by 0.001, round, divide by 0.001

This is particularly useful in data reporting, financial projections, and population statistics where exact figures are less meaningful than order-of-magnitude accuracy.

Rounding errors and floating-point arithmetic

Computers store most decimal fractions as binary floating-point numbers, which cannot exactly represent many decimals (e.g., 0.1 in binary is a repeating fraction). This means naively multiplying and dividing to round can produce artifacts like 2.35 → 2.3499… instead of 2.4. This calculator uses parseFloat(result.toFixed(dp)) as a final step to correct these drift errors, ensuring the display matches mathematical expectations.