Scientific Notation Calculator

Scientific notation writes a number as a coefficient multiplied by a power of ten. The coefficient is at least 1 and less than 10, and the exponent counts how far the decimal point moved. So 6000 becomes 6 × 10^3, and 0.000452 becomes 4.52 × 10^-4. A positive exponent means a large number, while a negative exponent means a number smaller than 1.

Scientists, engineers and students use this format because it keeps the size of a number visible at a glance. It also makes significant figures explicit, since every digit in the coefficient counts. Calculators and programming languages use a shorter cousin called E notation, where 4.52 × 10^-4 appears as 4.52e-4. Engineering notation is a third variant that keeps exponents in steps of three.

Type a number into the Convert tab in any common format. Plain decimals like 0.00047, written forms like 4.7 × 10^-4 or 4.7x10^-4, and E notation like 4.7e-4 are all accepted. The tool shows the scientific, E, engineering and standard forms at the same time. Spaces between digit groups are ignored, so 149 597 870 700 works too.

Use the Significant figures menu to round the result, or leave it on Auto to keep every digit you entered. The Calculate tab takes two numbers and an operator, and the Swap button reverses their order for subtraction and division. Each result has its own copy button, so you can paste the exact form you need. For whole expressions with brackets, use the math calculator instead.

To convert, the calculator moves the decimal point until exactly one nonzero digit sits to its left. Each move to the left adds one to the exponent, and each move to the right subtracts one. For 0.000452, the point moves four places right, so the exponent is -4. The number of moves is always shown in the steps panel.

Normalization fixes coefficients that fall outside the 1 to 10 range after arithmetic. A product like 30 × 10^7 is correct but not normalized, so the tool rewrites it as 3 × 10^8. Addition and subtraction first rewrite both numbers with the same exponent, then combine the coefficients. Engineering notation instead picks the nearest exponent that is a multiple of three.

These examples cover conversion, arithmetic, rounding and the SI prefixes used in engineering. Each one gives the exact input, the output and what the result tells you. They start with simple conversions, then move to arithmetic and real physical constants. The exponent alone reveals a number's order of magnitude, which is why scientists compare sizes by exponent before reading the full coefficient.

Paste any input into the tool above to check it, and enable Show Steps to compare the explanation with the live trace. Constants come from the SI values published by NIST.

JavaScript formats numbers with toExponential and toPrecision, and it switches to E notation automatically for values of 10^21 and above or below 10^-6. Python uses format specifiers like .2e and always pads the exponent to at least two digits. Both languages store numbers as IEEE 754 doubles, so very long coefficients lose their last digits.

For exact values, Python's Decimal type and JavaScript libraries such as big.js keep every digit you supply. That is the approach this tool uses, which is why 1.602176634 × 10^-19 expands to its full decimal without rounding. Format for display only at the very end of a calculation. Rounding in the middle of a long chain of steps lets small errors pile up.

// Format a number in E notation
(0.000452).toExponential();     // "4.52e-4"
(299792458).toExponential(2);   // "3.00e+8"
(149597870700).toPrecision(3);  // "1.50e+11"

// JavaScript switches to E notation on its own
console.log(1e21);      // 1e+21
console.log(0.000001);  // 0.000001
console.log(1e-7);      // 1e-7

from decimal import Decimal

print(f"{0.000452:.2e}")        # 4.52e-04 (Python pads the exponent)
print(f"{299792458:.3e}")       # 2.998e+08
print(Decimal("6.02214076e23"))  # 6.02214076E+23
print(format(Decimal("1.602176634e-19"), "f"))  # 0.0000000000000000001602176634

Every conversion runs as exact decimal arithmetic in your browser, so no coefficient is silently truncated. Rounding happens only when you choose a number of significant figures, and it uses round half up. Exponents from -999 to 999 are supported, which covers every physical constant and most astronomy data.

Nothing you type is sent to a server, logged or stored, and the page makes no network requests with your numbers. Constants quoted on this page follow NIST Special Publication 330, the US edition of the SI brochure. SI prefix names follow the same source, including ronna and quetta added by the CGPM in 2022. The same privacy rules apply to all the math calculators on this site.

Most errors come from a coefficient outside the 1 to 10 range or an exponent with the wrong sign. Another frequent slip is counting leading zeros as significant figures. The table lists these mistakes together with the messages the tool shows for invalid input.

Confusing the calculator E with the constant e is also common, since both appear on scientific keypads. In this tool, e or E between digits always means times ten to the power. The mathematical constant e is not accepted here; use the calculator with eˣ and logarithms.

Each notation serves a different reader. Standard form is best for everyday amounts, and scientific notation suits physics and chemistry. E notation is what software and calculator screens print, while engineering notation lines up with SI prefixes like kilo, mega and micro.

This scientific notation calculator shows all four forms at once. That lets you move between a textbook, a spreadsheet and a datasheet without converting by hand. Use the table below to pick the right form for your task.