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Browse all calculatorsType a number in any form to see it in scientific, E and engineering notation, or add, subtract, multiply and divide in scientific notation. Exact results, with the working shown.
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All digits keeps the exact value. A number rounds and pads the result to that many significant figures. Match inputs (Calculate only) follows the textbook rules for multiplying, dividing, adding and subtracting.
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A scientific notation calculator writes any number as a × 10n, with a between 1 and 10, and does arithmetic on numbers in that form. This one also gives E notation and engineering notation, handles very large and very small values exactly, and shows the working for every step.
Type or paste a number in any common form, such as 1568938, 6.022e23, 6.022 × 10^23 or 6.022 × 10²³, and it appears in all four notations at once. Switch to Calculate to add, subtract, multiply or divide two numbers. The maths uses exact decimal digits, not floating point, so 0.1 + 0.2 is exactly 0.3. To trim a result to fewer digits, see the rounding calculator, and for counting digits use the significant figures calculator.
| Typed as | Scientific | E notation | Engineering |
|---|---|---|---|
| 1568938 | 1.568938 × 106 | 1.568938e6 | 1.568938 × 106 |
| 0.00000345 | 3.45 × 10−6 | 3.45e-6 | 3.45 × 10−6 |
| 4500 | 4.5 × 103 | 4.5e3 | 4.5 × 103 |
| −0.00057 | −5.7 × 10−4 | −5.7e-4 | −570 × 10−6 |
| 6.02214076e23 | 6.02214076 × 1023 | 6.02214076e23 | 602.214076 × 1021 |
| 1.602176634e−19 | 1.602176634 × 10−19 | 1.602176634e-19 | 160.2176634 × 10−21 |
The last two rows are the values NIST lists for the Avogadro constant (per mole) and the elementary charge (in coulombs), both exact.
The first answer is already on screen. Change any number and every result updates at once, with no Calculate button to press.
Convert shows one number in scientific, E, engineering and decimal form. Calculate takes two numbers, X and Y, and an operation: add, subtract, multiply or divide.
Any form works: 1568938, 0.00000345, 6.022e23 or 6.022 × 10^23. On a phone, tap the ×10^, e and minus buttons beside the box instead of hunting for symbols.
Each notation has its own Copy button. The line under the result says whether the answer is exact, and how many significant figures it has.
Open Show the working to see every step, from matching exponents to normalising. Choose 3, 4, 6 or your own number of significant figures, or Match inputs.
Scientific notation keeps a number as a coefficient and a power of ten. To convert by hand, move the decimal point until one non-zero digit stands in front of it. Count the places moved: left for a positive exponent, right for a negative one. So 1,568,938 is 1.568938 × 106 and 0.00000345 is 3.45 × 10−6.
For arithmetic, the exponents do most of the work. Multiplying adds them and dividing subtracts them, while adding and subtracting first needs the same exponent on both numbers. Afterwards, shift the coefficient back into the range 1 to 10. The fraction calculator is the better tool when the numbers are fractions rather than powers of ten.
| Operation | Rule | Result |
|---|---|---|
| Add or subtract | Give both numbers the same exponent, then add or subtract the coefficients | 1.23 + 0.0000345 = 1.2300345, so 1.2300345 × 107 |
| Multiply | Multiply the coefficients and add the exponents | 1.23 × 3.45 = 4.2435 and 7 + 2 = 9, so 4.2435 × 109 |
| Divide | Divide the coefficients and subtract the exponents | 1.23 ÷ 3.45 ≈ 0.35652 and 7 − 2 = 5, so 3.5652 × 104 |
| Normalise | If the coefficient is outside 1 to 10, shift the point and change the exponent | 12.3 × 105 = 1.23 × 106 |
Three ways to write the same number. Engineering notation uses exponents that are multiples of 3, which match the SI prefixes.
| Notation | Pattern | Exponent rule | Example |
|---|---|---|---|
| Scientific (normalised) | a × 10n | a is at least 1 and below 10, n is a whole number | 4.5 × 104 |
| E notation | aen | The same as scientific, with e standing for times ten to the power of | 4.5e4 |
| Engineering | a × 10n | n is a multiple of 3, so a runs from 1 to just under 1000 | 45 × 103 |
| Decimal (real number) | digits | No exponent, every digit written out | 45000 |
| Power of ten | Prefix | Symbol | Power of ten | Prefix | Symbol |
|---|---|---|---|---|---|
| 10−3 | milli | m | 103 | kilo | k |
| 10−6 | micro | μ | 106 | mega | M |
| 10−9 | nano | n | 109 | giga | G |
| 10−12 | pico | p | 1012 | tera | T |
| 10−15 | femto | f | 1015 | peta | P |
| 10−18 | atto | a | 1018 | exa | E |
| 10−21 | zepto | z | 1021 | zetta | Z |
| 10−24 | yocto | y | 1024 | yotta | Y |
The SI also has ronna (R, 1027), quetta (Q, 1030), ronto (r, 10−27) and quecto (q, 10−30). The calculator names them in the line under the result.
Many scientific notation calculators convert one way, or ask for a coefficient and an exponent in separate boxes and stop at the answer. These are the details that change what you get.
| Feature | Many basic calculators | This calculator |
|---|---|---|
| Results | Press a button to see an answer | Updates as you type, with an answer on first load |
| Input | One format, or separate coefficient and exponent boxes | Decimal, E notation, × 10^n, superscripts or a paste from a textbook |
| Notations shown | Often scientific only, sometimes E notation | Scientific, E, engineering and decimal, each with a Copy button |
| Arithmetic | Floating point, which can add rounding noise | Exact decimal digits; a division is cut at 20 digits only when it never ends |
| Significant figures | Decimal places only, or none | 1 to 50 significant figures, or Match inputs for the textbook rules |
| Working | The answer only | Every step written out, including aligning exponents and normalising |
| Limits and errors | Often not stated | 400 digits and exponents from −9999 to 9999, with plain messages for bad input |
| Sharing | Rare | Copy any form, or share a link that opens with the same numbers |
Enter constants such as 6.02214076e23 and 1.602176634e-19 and multiply them. The product is exactly 9.64853321233100184 × 104, with no rounding noise.
Check an answer, read the steps, and use Match inputs to see how the significant figure rules change the last digit.
Engineering notation lines the exponent up with the SI prefixes, so 4.7e-9 reads as 4.7 × 10−9, a nano value.
Programs and spreadsheets print big and small numbers in E notation. Paste 2.5E+6 or 1e-9 to see the plain decimal, or the reverse.
Divide one huge number by another to see how many times larger it is, or compare a distance and a width written as powers of ten.
Paste what a handheld calculator shows, such as 1.23E7, and read the same value in every notation. Then try the percentage calculator for the change between two results.
Most mistakes with scientific notation come from the same few places. These are the ones this calculator is built to handle.
In 6.022e23 the e means times ten to the power of. It is not the mathematical constant, so 1e3 is exactly 1000.
Zeros you type after a decimal point are kept, because they count as significant figures. Zeros at the end of a whole number such as 4500 are treated as placeholders.
A negative exponent means a number below 1. 10−3 is 0.001, and 1.6 × 10−19 has eighteen zeros after the point.
If an answer comes out as 12.3 × 105, it is rewritten as 1.23 × 106. The working shows the shift.
JavaScript and Python store decimals in binary, so 0.1 is only approximate. Here the digits are whole numbers, so sums and products come out exact.
Some courses, for example in the UK, call scientific notation standard form, while others use that name for the ordinary written number. Check which one your course means.
Each number can have up to 400 digits and an exponent from −9999 to 9999. Longer input shows a message instead of a wrong answer.
1 ÷ 3 has no last digit, so the quotient is cut to 20 significant digits and marked with ≈. Choose a larger number of significant figures, up to 50, to see more.
There are no powers, roots or logarithms. To round a long result, use the rounding calculator, and to count digits use the significant figures calculator.
The conversions and rules follow the standard definitions, and the calculator is checked against thousands of results computed separately with Python decimal arithmetic. The definitions and values come from these references.
Short answers to common questions about scientific, E and engineering notation.
Scientific notation writes a number as a × 10^n, where the coefficient a is at least 1 and less than 10 and the exponent n is a whole number. For example, 4500000 is 4.5 × 10^6 and 0.00032 is 3.2 × 10^-4.
Move the decimal point until one non-zero digit is in front of it, then count the places you moved it. Moving the point left gives a positive exponent and moving it right gives a negative one. For 1568938 the point moves 6 places left, so the answer is 1.568938 × 10^6.
Move the decimal point as many places as the exponent says, to the right for a positive exponent and to the left for a negative one, adding zeros where needed. So 3.45 × 10^-6 is 0.00000345 and 6.022e23 is 602200000000000000000000. The Decimal line of the result shows this for you.
E notation writes × 10^ as the letter e, so 6.022e23 means 6.022 × 10^23. The e here is not the mathematical constant e, so 1e3 is simply 1000. Calculators, spreadsheets and programming languages print very large and very small numbers this way.
Engineering notation is scientific notation with an exponent that is always a multiple of 3, so the coefficient runs from 1 up to just under 1000. For example, 45000 is 4.5 × 10^4 in scientific notation and 45 × 10^3 in engineering notation. The multiples of 3 line up with SI prefixes such as kilo, mega and nano.
Rewrite both numbers with the same exponent, add or subtract the coefficients, then normalise the result. For 1.23 × 10^7 + 3.45 × 10^2, write the second number as 0.0000345 × 10^7, add to get 1.2300345 × 10^7, and the coefficient is already between 1 and 10. The working section shows each of these steps.
To multiply, multiply the coefficients and add the exponents. To divide, divide the coefficients and subtract the exponents. If the new coefficient is not between 1 and 10, shift the decimal point and change the exponent to match, for example 12.3 × 10^5 = 1.23 × 10^6.
Every digit in the coefficient counts, so 3.20 × 10^4 has three. The calculator shows the count under the result. Zeros you type after a decimal point are kept, but zeros at the end of a whole number such as 4500 are treated as placeholders, so 4500 reads as 4.5 × 10^3 with two. Type 4500. or 4.500e3 to keep all four.
It applies the usual textbook significant figure rules to the result. When multiplying or dividing, the answer keeps as many significant figures as the input that has the fewest. When adding or subtracting, it is rounded to the least precise place of the two inputs. Pick 3, 4, 6 or a custom number instead to set the count yourself.
Most software stores decimals as binary floating point numbers, which cannot hold values such as 0.1 exactly, so sums can drift: in JavaScript 0.1 + 0.2 gives 0.30000000000000004. This calculator keeps the digits as whole numbers and works on them exactly, so 0.1 + 0.2 is 0.3 and 6.022e23 × 1.6e-19 is exactly 96352.
Type a minus sign after the e or the power sign, as in 1.6e-19 or 1.6 × 10^-19, or tap the minus button beside the box on a phone. Each number can have up to 400 digits and an exponent from -9999 to 9999. A division that never ends, such as 1 ÷ 3, is cut to 20 significant digits and marked with an approximately equal sign.
No. The conversion and the arithmetic run in your browser and nothing is sent to a server. After you change a value the numbers are added to the page address after the # sign, which is not sent to the site, so you can copy a link that reopens the same numbers.