Rounding Calculator – Round Numbers, Decimals & Significant Figures

Q: What does this rounding calculator do?

The rounding calculator lets you round any real number using several different methods: to a set number of decimal places, to a specified multiple, or to a chosen number of significant figures. You can also choose the rounding rule: nearest (half up), bankers rounding (half to even), always up, always down, toward zero, or away from zero.

Q: What is the difference between rounding up, rounding down and rounding to nearest?

Rounding up always moves the number toward positive infinity, rounding down always moves it toward negative infinity, while rounding to nearest moves the number to the closest representable value. When the number is exactly halfway between two candidates, different conventions apply: half up always rounds away from zero, while bankers rounding rounds to the nearest even last digit to reduce systematic bias.

Q: When should I use significant figures instead of decimal places?

Use significant figures when you need to reflect the precision of a measurement or a physical constant, regardless of its magnitude. For example, 0.001234 and 12340 can both be expressed with four significant figures. Rounding to decimal places is more convenient for prices, financial values or situations where the position of the decimal point is fixed.

Q: Can I use this tool for financial or regulatory reporting?

The calculator is designed for learning, everyday use and quick checks. Financial statements, tax returns and regulatory filings often specify their own rounding rules that may differ by jurisdiction. Always follow the rounding conventions explicitly required by your standards, laws or internal policies, and verify results with your accounting or compliance advisor.

What is rounding?

Rounding is the process of replacing a number with a nearby value that has fewer digits or a more convenient format. We do it all the time: prices to cents, time to the nearest 5 minutes, measurements to a sensible number of significant figures.

A good rounding rule should be clearly defined and applied consistently. This calculator makes the rule explicit so you can see exactly what is happening.

Common rounding rules implemented here

1. Rounding to decimal places (half up)

Rounding to \(d\) decimal places is based on the factor \(10^d\). Let \(x\) be your original number. The standard "half up" rule is:

\[ \text{round}_{\text{half up}}(x, d) = \frac{\operatorname{round}\!\bigl(x \cdot 10^d\bigr)}{10^d}, \]

where round means "round to nearest, 0.5 away from zero" (the usual computer and calculator rule). For example, \( 2.345 \) rounded to 2 decimal places is \( 2.35 \).

2. Bankers rounding (half to even)

Bankers rounding (also called "round half to even") is used to reduce statistical bias when you are rounding many values (for example in statistics or finance).

If the digit after the last kept position is < 5: round as usual.
If it is > 5: round away from zero.
If it is exactly 5 with nothing but zeros after it: round to make the last kept digit even.

For instance, with two decimals: \( 2.345 \rightarrow 2.34 \) (because 4 is even), but \( 2.355 \rightarrow 2.36 \) (because 5 is odd, so we make it even).

3. Rounding up, down, toward or away from zero

When you always round in the same direction you are applying a directed rounding rule:

Up (ceiling): always round toward \(+\infty\).
Down (floor): always round toward \(-\infty\).
Toward zero: drop the extra digits, making the result closer to zero.
Away from zero: push the value farther from zero.

These are often used in regulations and contracts. For example, a policy may require rounding up to the next cent (ceiling) so a customer never underpays.

4. Rounding to a multiple

Sometimes the unit is not a power of ten, but another step size: the nearest 5 km/h, 0.05 € (fuel prices), 15 minutes, 500 units, and so on. If \(m\) is your step size, you can round with:

\[ \text{round to multiple}(x, m) = m \cdot \operatorname{round}\!\left(\frac{x}{m}\right). \]

5. Rounding to significant figures

Significant figures focus on the meaningful digits, not the position of the decimal point. For a non-zero number \(x\) and a target of \(s\) significant figures:

\[ x = \pm a \times 10^k, \quad 1 \le |a| < 10, \] and you round the mantissa \(a\) to \(s\) digits, then scale back.

This is standard in science and engineering, where measurement precision matters more than the exact decimal representation.

Examples you can try

Money: \( 12.345 \) to 2 decimals (half up) → \( 12.35 \).
Bankers rounding: \( 2.345 \) (2 decimals) → \( 2.34 \), but \( 2.355 \) → \( 2.36 \).
Time: 12 minutes to nearest multiple of 5 → 10; 13 → 15.
Significant figures: 0.001234 to 3 s.f. → 0.00123; 12340 to 3 s.f. → 1.23 × 10⁴.

FAQ: using the rounding calculator correctly

What does this rounding calculator do?

It rounds a single real number using several different and clearly documented rules: decimal places, significant figures, rounding to a multiple, and various directions (nearest, up, down, toward/away from zero). It also reports the absolute and relative rounding error so you can see how much information you lose.

What is the difference between rounding up, rounding down and rounding to nearest?

Rounding to nearest chooses the closest representable value. Rounding up always moves toward \(+\infty\), and rounding down always moves toward \(-\infty\), even if that means the result is further from the original value. When the number is exactly halfway between two candidates, the rule needs to specify what to do (half up, half to even, etc.).

When should I use significant figures instead of decimal places?

Use significant figures whenever you want the number of meaningful digits to reflect measurement precision, for example in physics and chemistry. Use decimal places when the decimal point is fixed and conventional, such as currency amounts or interest rates.

Can I use this tool for financial or regulatory reporting?

You can use it as a quick check, but official documents usually have their own specific rounding rules. Always follow the requirements in your accounting standards, contracts, tax codes or regulatory guidance, and confirm with a professional when needed.

Interactive rounding workspace