Significant figures calculator, every digit marked.

A significant figures calculator counts the digits in a number that carry information about how precisely it was measured. 0.00450 has 3 significant figures, 1500 has 2, and 1500. (with a point) has 4. This calculator marks each digit as counted or not, shows the rule that applied, rounds to any number of sig figs, and does addition, subtraction, multiplication and division while keeping the answer to the right precision.

How to use the significant figures calculator

1. Stay on Count and round and type a value in Number. You can write 0.00450, 1500, 1500., 1.20e5 or 1.20 × 10^5.
2. Read the big card for the count. The digits below it are shaded: bright digits count, dim ones do not. Each rule is listed under Why each digit counts or not.
3. To round, type a number in Round to this many sig figs. The rounded value appears in its own card, in scientific notation when plain text would hide a zero that counts.
4. To work with two measurements, press Calculate, type Number A and Number B, and pick an Operation. The answer and each step appear on the right.
5. Use Use the answer as A to carry an answer into the next sum. Press Copy result or Copy link to keep your work.

The counting rules, with examples

• Nonzero digits always count. 4.56 has 3.
• Zeros between counted digits count. 2003 has 4.
• Leading zeros never count. They only show where the decimal point sits. 0.00450 has 3, not 6.
• Trailing zeros after a decimal point count. 0.00450 keeps its last zero, and 100.0 has 4.
• Trailing zeros in a whole number without a point are unclear. 1500 is usually read as 2 significant figures. Write 1500. for 4, or 1.50 × 10^3 for 3. The box Count zeros at the end of a whole number reads such zeros as counted.

The power of ten in scientific notation is never counted. 1.20 × 10^5 has 3, the same as 1.20.

Rounding to n significant figures

Keep the first n counted digits and look at the next one. Round up if it is 5 or more, and down if it is less. 0.0045678 to 3 significant figures is 0.00457. 123456 to 2 is 120000, but that reads as 2 only by convention, so the calculator shows 1.2 × 10^5. When you need more figures than a number has, zeros are added: 2.5 to 4 is 2.500.

Choose Half to even if your course rounds exact ties to the even digit. 2.665 to 3 gives 2.67 half up but 2.66 half to even, because 6 is even. Most school work uses half up.

Adding and subtracting

The answer is kept to the coarsest place of any number in the sum. 12.11 + 18.0 is exactly 30.11. 12.11 reaches the hundredths and 18.0 only the tenths, so the answer is rounded to the tenths: 30.1. For 5.673 − 2.1 the exact answer is 3.573, which becomes 3.6. A whole number with unclear zeros limits the answer too: 100 + 0.123 gives 100, because 100 is only known to the hundreds place.

Multiplying and dividing

The answer has as many significant figures as the number with the fewest. 4.56 × 1.4 is exactly 6.384. 1.4 has 2, so the answer is 6.4. 25.0 ÷ 3.00 is 8.3333 and both numbers have 3, so it is 8.33. An answer such as 2.50 × 4.0, which is 10 with 2 figures, is written 1.0 × 10^1 so that the zero is seen to count.

Exact numbers

A count (12 eggs) or a defined factor (2.54 cm per inch) is exact and has no uncertainty, so it must not limit the answer. Tick A is exact or B is exact. Then 12 × 3.46 gives 41.5, kept to the 3 figures of 3.46, not to the 2 of the 12.

A lab example from start to finish

A beaker holds 24.35 g when full and 12.1 g when empty. Subtracting gives 12.25, which is rounded to the tenths place because 12.1 stops there, so the mass of liquid is 12.3 g half up (12.2 g with half to even, because the tie goes to the even digit). The liquid fills 8.0 mL. Dividing 12.3 by 8.0 gives 1.5375. Both numbers have 2 significant figures, so the density is 1.5 g/mL. If the volume had been read as 8.00 mL, the answer would carry 3 figures and be 1.54 g/mL. One extra zero on a reading changes the answer.

Keep the rule for each step in mind

In a longer calculation, mixed steps are common. Work out an addition or subtraction first and keep its place, then use the count of figures it leaves for the multiplication that follows. Round at the very end, and use the Use the answer as A button only when you want to treat a rounded answer as a new measurement.

Common problems

• The calculator gives a different count than your book for 1500. Textbooks differ on end zeros without a point. Add a point or use scientific notation to remove the doubt.
• The answer to a subtraction has fewer figures than either number. That is correct. 5.673 − 5.6 is 0.1, because the tenths place limits it.
• Round only at the end. Rounding between steps adds error. This calculator works exactly and rounds once.

For general sums use the scientific calculator, and for the spread of a set of measurements try the standard deviation calculator.