Standard Form Calculator
Enter a number in ordinary decimal form and the calculator rewrites it in standard form, a number from 1 to 10 multiplied by a power of ten, together with the matching e-notation.
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Created by the Reeliy Editorial Team. Last updated: Oct 19, 2026
What is standard form?
Standard form is a compact way to write very large or very small numbers. A number is written as a coefficient a multiplied by a power of ten, where the coefficient is at least 1 and less than 10 (in absolute value) and the exponent n is a whole number.
N = a × 10n, with 1 ≤ |a| < 10 and n an integer
In the United Kingdom and several other countries this layout is taught as “standard form”. Elsewhere, and in science and engineering, the same thing is called scientific notation. The two names describe an identical format, so this page and our scientific notation calculator agree.
The exponent records how far the decimal point has moved. A positive exponent means a number of 10 or more, a negative exponent a number below 1, and an exponent of 0 a number between 1 and 10.
How to write a number in standard form
- Find the first non-zero digit and place the decimal point just after it. This gives the coefficient a.
- Count how many places the decimal point moved from its original position.
- If it moved left (the original number was 10 or more), the exponent is positive and equals that count. If it moved right (the number was below 1), the exponent is negative.
- Write the coefficient, the multiplication sign and 10 raised to the exponent.
Example 1: 4,560,000. The decimal point sits after the last 0. Moving it six places left gives 4.56, so the number is 4.56 × 106.
Example 2: 0.000072. The first non-zero digit is the 7, which is five places to the right of the original point. The number is 7.2 × 10−5.
Example 3: 12,500 is not written 12.5 × 103, because 12.5 is larger than 10. Shift one more place and the correct standard form is 1.25 × 104.
| Number | Standard form | e-notation |
|---|---|---|
| 8,700,000,000 | 8.7 × 109 | 8.7e+9 |
| 299,792,458 | 2.997925 × 108 | 2.997925e+8 |
| 0.0305 | 3.05 × 10−2 | 3.05e-2 |
| −450 | −4.5 × 102 | −4.5e+2 |
| 5 | 5 × 100 | 5e+0 |
Using the calculator
Type a number into the field and press the button. You can enter ordinary decimals (0.00032), whole numbers (12345), negative numbers and numbers already written in e-notation (1.5e10). Use a dot as the decimal separator and no thousands separators.
Two results are returned. Scientific notation shows the coefficient and the power of ten, and Scientific e notation shows the same value in the compact form used by spreadsheets and programming languages, where 1.2345e+4 means 1.2345 × 104.
The coefficient is rounded to six decimal places and trailing zeros are dropped, so 100 gives 1 × 102 rather than 1.000000 × 102. Zero is the one input it cannot convert: there is no first non-zero digit to anchor the exponent, so the calculator asks for a non-zero number.
Calculating with standard form
Powers of ten make some arithmetic quick. Work on the coefficients and the exponents separately, then tidy the result so the coefficient is between 1 and 10 again.
(a × 10m) × (b × 10n) = (a × b) × 10m+n
(a × 10m) ÷ (b × 10n) = (a ÷ b) × 10m−n
Multiplying: (3 × 104) × (2.5 × 10−2) = 7.5 × 102, which is 750. Dividing: (6.4 × 105) ÷ (8 × 102) = 0.8 × 103, and since 0.8 is below 1 the answer is rewritten as 8 × 102.
Adding or subtracting needs matching exponents first. To add 3.2 × 104 and 5 × 103, rewrite the second term as 0.5 × 104. The sum is 3.7 × 104, or 37,000.
Common mistakes
- Leaving the coefficient outside the range 1 to 10, such as 45 × 103 or 0.45 × 105.
- Using the wrong sign on the exponent. Small numbers get negative exponents, large numbers positive ones.
- Counting from the wrong end of the number: count the places the point moves, not the digits in the number.
- Reading 10−3 as −1000. A negative exponent means a reciprocal: 10−3 = 1/1000 = 0.001.
- Confusing the “e” in e-notation with Euler’s number. In 1.5e10 it just stands for “times ten to the power”.
To count significant figures in a value you have converted, see the significant figures calculator.
Where standard form is used
- Astronomy and physics, where distances, masses and constants span dozens of orders of magnitude: the speed of light is about 2.998 × 108 m/s and an electron’s mass about 9.109 × 10−31 kg.
- Chemistry, for counts of particles such as Avogadro’s number, 6.022 × 1023 per mole.
- Computing, where results of floating-point calculations are printed in e-notation.
- Everyday comparison of sizes, from the width of a hair to the population of a country.
Frequently asked questions
Is standard form the same as scientific notation?
Yes. “Standard form” is the name used in the UK and some other school systems; “scientific notation” is the common name elsewhere. Both write a number as a coefficient from 1 to less than 10 times a power of ten.
How do I write 0.00045 in standard form?
Move the decimal point four places to the right to get 4.5, and use a negative exponent: 4.5 × 10−4.
What does 3.2e+6 mean?
It is e-notation for 3.2 × 106, which equals 3,200,000. The e stands for “times ten to the power of”.
Why does the calculator not accept zero?
Zero has no first non-zero digit, so no exponent can bring the coefficient into the range 1 to 10. Zero is simply written 0, or if you must, 0 × 100.
References
Cite this calculator and page
If you use this page in your work, you can cite it as:
Reeliy Editorial Team. (2026). Standard Form Calculator. Reeliy. https://reeliy.com/calculators/standard-form-calculator“Standard Form Calculator.” Reeliy, 2026, https://reeliy.com/calculators/standard-form-calculator.