Standard Form Calculator
Enter any number and this calculator instantly converts it to standard form (scientific notation), E-notation, engineering notation, and back to ordinary decimal. It shows every step of the conversion so you can follow the working. Use the significant-figures slider to control precision, and choose whether to convert a decimal number to standard form or go the other direction from scientific notation to ordinary form.
What is standard form?
Standard form (also called scientific notation) is a way to write very large or very small numbers compactly. A number in standard form is written as a x 10^n, where a is a number between 1 and 10 (the coefficient) and n is a whole-number exponent. For example, the speed of light (299,792,458 m/s) becomes 2.998 x 10^8 in standard form, and the charge on an electron (0.0000000000000000001602 C) becomes 1.602 x 10^-19. In UK mathematics education "standard form" always means this a x 10^n format. In North American usage the same format is called "scientific notation," while "standard form" can mean ordinary decimal notation.
How to convert a number to standard form
To convert a decimal number to standard form, move the decimal point left or right until exactly one non-zero digit sits to its left. Count the number of places you moved: if you moved left, the exponent is positive (the original number was large); if you moved right, the exponent is negative (the original number was small). Write the result as the coefficient (the adjusted number) multiplied by 10 raised to that exponent. Example: 45,600 becomes 4.56 x 10^4 because you move the decimal four places left. Example: 0.00307 becomes 3.07 x 10^-3 because you move the decimal three places right.
E-notation and engineering notation
E-notation (or calculator notation) writes the same information as aEn, for example 2.998E8 instead of 2.998 x 10^8. This is widely used in programming and on calculators where superscript characters are not available. Engineering notation is a variant of standard form in which the exponent must be a multiple of three. This aligns the exponent with the SI metric prefixes (kilo = 10^3, mega = 10^6, giga = 10^9, etc.), making unit conversions straightforward. For 45,600 the engineering form is 45.6 x 10^3, not 4.56 x 10^4, because 3 is the largest multiple of 3 not exceeding 4.
Significant figures in standard form
Standard form makes significant figures explicit. Every digit in the coefficient counts as a significant figure. Trailing zeros after the decimal point in the coefficient ARE significant: 3.50 x 10^5 has three significant figures, while 3.5 x 10^5 has only two. Use the significant-figures selector above to control how many figures appear in your coefficient. A result in standard form should carry only as many significant figures as the original measurement contains.
Common powers of 10 and SI prefixes
| Power | Value | SI prefix | Symbol | Example |
|---|---|---|---|---|
| 10^24 | 1,000,000,000,000,000,000,000,000 | yotta | Y | Mass of Earth ~6 x 10^24 kg |
| 10^21 | 1,000,000,000,000,000,000,000 | zetta | Z | Stars in the observable universe ~10^21 |
| 10^18 | 1,000,000,000,000,000,000 | exa | E | 1 exabyte = 10^18 bytes |
| 10^15 | 1,000,000,000,000,000 | peta | P | Light-year ~9.46 x 10^15 m |
| 10^12 | 1,000,000,000,000 | tera | T | 1 terabyte = 10^12 bytes |
| 10^9 | 1,000,000,000 | giga | G | 1 gigabyte = 10^9 bytes |
| 10^6 | 1,000,000 | mega | M | 1 megawatt = 10^6 watts |
| 10^3 | 1,000 | kilo | k | 1 kilogram = 10^3 grams |
| 10^0 | 1 | (none) | Everyday human scale | |
| 10^-3 | 0.001 | milli | m | 1 millimetre = 10^-3 m |
| 10^-6 | 0.000001 | micro | u | 1 micrometre = 10^-6 m |
| 10^-9 | 0.000000001 | nano | n | Wavelength of UV light ~10^-9 m |
| 10^-12 | 0.000000000001 | pico | p | 1 picofarad = 10^-12 F |
| 10^-15 | 0.000000000000001 | femto | f | Proton radius ~0.85 x 10^-15 m |
Engineering notation always uses exponents that match these SI prefixes.
Frequently asked questions
What is the difference between standard form and scientific notation?
They are the same format (a x 10^n, with 1 <= a < 10), just called different names in different countries. In the UK, Australia, New Zealand, and much of the Commonwealth, "standard form" is the curriculum term. In North America, the same notation is almost always called "scientific notation." This calculator uses both terms interchangeably.
How do I convert a number to standard form by hand?
Move the decimal point left (for large numbers) or right (for small numbers) until one non-zero digit sits to the left of the decimal. Count the number of places moved: left movement gives a positive exponent, right movement gives a negative exponent. Write the result as that adjusted number (the coefficient) multiplied by 10 raised to the exponent you counted. For example, 0.00042 becomes 4.2 x 10^-4 after moving the decimal four places right.
What is engineering notation and when should I use it?
Engineering notation restricts the exponent to multiples of three (0, 3, 6, -3, -6, etc.) so it always aligns with SI prefixes such as kilo, mega, giga, milli, and micro. This makes unit conversions very direct: 4.7 x 10^3 ohms is 4.7 kilohms. Use engineering notation in electronics, electrical engineering, and any context where you frequently convert between SI-prefixed units.
What counts as a "standard form" number?
A number is in proper standard form when the coefficient satisfies 1 <= |a| < 10. So 3.7 x 10^5 is valid, but 37 x 10^4 is not (because 37 >= 10) and 0.37 x 10^6 is not (because 0.37 < 1). They all represent the same value, only the first form is correct standard form.
How do I add or subtract numbers in standard form?
Make both numbers use the same power of 10 first, then add or subtract the coefficients. For example, 3.2 x 10^5 plus 4.7 x 10^4: convert the second to 0.47 x 10^5, then add the coefficients: 3.2 + 0.47 = 3.67, giving 3.67 x 10^5. If the result has a coefficient outside 1 to 10, adjust the exponent accordingly.
How do I multiply or divide numbers in standard form?
Multiply (or divide) the coefficients, then add (or subtract) the exponents. For example, (3.0 x 10^8) x (4.0 x 10^-6) = (3.0 x 4.0) x 10^(8 + -6) = 12.0 x 10^2 = 1.20 x 10^3. Always check that the final coefficient is between 1 and 10, adjusting the exponent if not.
What is E-notation?
E-notation (or scientific E-notation) is a plain-text way to write the same thing as scientific notation when superscripts are not available. The letter E replaces "x 10^", so 2.998 x 10^8 becomes 2.998E8, and 1.602 x 10^-19 becomes 1.602E-19. Most programming languages and calculators accept this format.