Scientific Calculator
Type the whole expression the way it looks in your notebook and get the result. It handles parentheses, powers, roots, logarithms, trigonometry in degrees, radians or gradians, and factorials, with the reasoning described step by step.
Educational use: results are estimates made for study and reference. Checking the answer and deciding what to do with it is the sole responsibility of whoever uses the tool. Read the legal notice.
On this page
- How to use the scientific calculator
- The circle that explains sine and cosine
- Examples to try in the calculator
- Order of operations and available functions
- Reference tables
- Common mistakes when using a scientific calculator
- Questions that come up while using it
- Before you trust the result
- Where a scientific calculator helps
- Terms you will come across
- From logarithm tables to your pocket
- Numerical curiosities
- More math tools
How to use the scientific calculator
Unlike single-operation calculators, here you write the whole expression on one line and the tool solves it following the order of operations. There is no need to press keys step by step and write down partial results.
- Write the expression in the field, using your device's keyboard or the on-screen buttons. The buttons insert text wherever the cursor is.
- Choose the angle unit. It only matters for sine, cosine, tangent and their inverses. The default is degrees.
- Set the decimal places, if you want a rounded result. In automatic mode, up to ten decimal places appear.
- Click Calculate (or press Enter). If something is wrong, the tool tells you what it didn't understand.
How to write each thing
- The four operations:
+-*(or ×) and/(or ÷). - Power:
2^10. The**symbol also works. - Roots:
sqrt(81)or√(81)for the square root,cbrt(27)for the cube root. - Logarithms:
log(1000)is base 10,ln(x)is the natural log, andlog(8; 2)uses the base you give after the semicolon. - Trigonometry:
sin,cos,tanand the inversesasin,acos,atan.senandtgare also valid. - Factorial:
5!. - Constants:
pi(or π),e(Euler's number) andphi(the golden ratio). - Percentage:
20%is worth 0.2. That is why200*15%gives 30.
Multiplication can be implicit, as in your notebook: 2pi, 3(4+5) and (1+2)(3+4) work. The tool calculates everything in your browser, and what you type is not sent anywhere.
The circle that explains sine and cosine
Sine and cosine come from a circle of radius 1. Mark an angle starting from the horizontal axis: the height of the point where the line touches the circle is the sine, and the horizontal distance to it is the cosine. For 30°, the sine is 0.5 and the cosine is about 0.866.
Examples to try in the calculator
1. The order of operations
What is 2 + 3 × 4? And (2 + 3) × 4?
Multiplication comes before addition, unless parentheses say otherwise. Type both and compare.
2. Power with parentheses
What is 2 × (3 + 4)^2?
Type 2*(3+4)^2 and the result is 98. Without the parentheses, 2*3+4^2 would give 22.
3. Compound interest by hand
$1,000 earning 5% per period, over 10 periods:
Type 1000*(1+5%)^10. This is a study exercise: real rates vary and depend on the terms of the contract.
4. Trigonometry in degrees
What are sin 30° and cos 60°?
With the unit set to degrees, just type the angle. To work in radians, change the unit and type sin(pi/6), which also gives 0.5.
5. Pythagoras in one go
The hypotenuse of a triangle with legs 3 and 4:
Type sqrt(3^2+4^2). For this kind of calculation there is also a dedicated tool, with a drawing of the triangle.
6. Factorials in combinations
In how many ways can you choose 3 people out of 10?
Type 10!/(3!*7!). The factorial grows very fast: 20! is already over 2 quintillion.
7. Logarithms
What are log 1000, log₂ 8 and ln(e²)?
The logarithm answers "what exponent do I raise the base to in order to reach this number?".
8. Scientific notation
Doubling Avogadro's constant, 6.02 × 10²³:
Use the letter e attached to the exponent to write powers of ten, as in 6.02e23.
Order of operations and available functions
What gets solved first
The tool follows the convention you learn in school, from what comes first to what comes last:
- Parentheses, from the inside out.
- Functions, such as sin, ln and √.
- Factorial (
!) and percentage (%). - Powers (
^), from right to left:2^3^2is 2^(3²) = 512. - Multiplication and division, from left to right.
- Addition and subtraction, from left to right.
Relationships the calculator uses
Implicit multiplication
When two terms appear side by side, they are multiplied in the same order as other multiplications, from left to right. So 1/2(3) becomes (1 ÷ 2) × 3 = 1.5. If you meant to divide by 2×3, write 1/(2*3). When in doubt, use parentheses.
Reference tables
Accepted functions and how to type them:
| Operation | How to type it | Example |
|---|---|---|
| Power | x^y | 2^10 = 1,024 |
| Square root | sqrt(x) or √(x) | sqrt(144) = 12 |
| Cube root | cbrt(x) | cbrt(-27) = −3 |
| Log base 10 | log(x) | log(100) = 2 |
| Log in another base | log(x; base) | log(81; 3) = 4 |
| Natural log | ln(x) | ln(1) = 0 |
| Exponential | exp(x) | exp(1) = e |
| Absolute value | abs(x) | abs(-7) = 7 |
| Remainder of a division | mod(a; b) | mod(17; 5) = 2 |
| Largest and smallest | max(a; b; …), min(...) | max(3; 9; 4) = 9 |
| Round | round(x; places) | round(2.675; 2) |
| Floor and ceiling | floor(x), ceil(x) | ceil(2.1) = 3 |
| Hyperbolic | sinh, cosh, tanh | sinh(0) = 0 |
Trigonometric values worth knowing by heart:
| Angle | Radians | Sine | Cosine | Tangent |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 0.5 | 0.8660 | 0.5774 |
| 45° | π/4 | 0.7071 | 0.7071 | 1 |
| 60° | π/3 | 0.8660 | 0.5 | 1.7321 |
| 90° | π/2 | 1 | 0 | undefined |
Common mistakes when using a scientific calculator
Angle in the wrong unit
The most frequent mistake. sin(30) gives 0.5 in degrees, but gives −0.988 in radians, because 30 rad is almost five and a half turns. Before calculating, check the unit you chose.
Forgetting parentheses in a division
1/2*3 gives 1.5, not 1/6. To divide by everything, write 1/(2*3). The same goes for the denominator of long fractions: whatever is under the fraction bar must go in parentheses.
Confusing −2² with (−2)²
Without parentheses, the minus sign is applied after the power, and the result is −4. With parentheses, the base is −2 and the result is 4.
Using a comma between arguments
Here the separator between arguments is the semicolon, not the comma, which can be confused with the thousands separator in numbers. Write log(8; 2), not log(8, 2).
Expecting % to work like on a pocket calculator
Here % simply divides by 100. So 50+10% gives 50.1, not 55. To add 10% to 50, write 50*(1+10%).
Square root of a negative number and log of zero
The square root of a negative number and the logarithm of zero or of a negative number do not exist among the real numbers. The calculator warns you instead of making up a result.
Blindly trusting very long decimals
Computers store numbers with about 15 to 16 significant digits. Calculations with many steps or gigantic numbers can show differences in the last decimal places. For studying it is irrelevant, but don't treat the final digits as if they were exact.
Questions that come up while using it
Does the calculator work in degrees or radians?
Both, and also in gradians. Choose the unit in the "Angle unit" field. It applies to sin, cos, tan and to the inverses asin, acos and atan, which return the angle in the chosen unit.
How do I calculate a square root?
Type sqrt(x) or √(x), for example sqrt(81) for 9. For other roots, use a fractional exponent: the fourth root of 16 is 16^(1/4), which gives 2.
What is the difference between log and ln?
log is the base-10 logarithm (log 1000 = 3) and ln is the natural logarithm, base e (ln e = 1). For another base, use log(x; base).
Why does sin(180) give 0 and not a tiny number?
Computers calculate sine with approximations, and the raw result for sin 180° would be something like 0.00000000000000012. The calculator rounds off these floating-point leftovers so that the known exact value, zero, shows up.
Why does the tangent of 90° give an error?
Because it doesn't exist. The tangent is sine divided by cosine, and the cosine of 90° is zero, which would lead to a division by zero. The same happens at 270° and equivalent angles.
How do I write a number in scientific notation?
Attach the letter e to the exponent, with no spaces: 3e8 is 3 × 10⁸, and 1.6e-19 is 1.6 × 10⁻¹⁹. Very large or very small results are also shown in this form.
What is the largest factorial that can be calculated?
170!, which is about 7.26 × 10³⁰⁶. From 171! on, the result exceeds the largest number the computer format can store, and the calculator warns you.
Can I use square brackets and curly braces?
Yes. Square brackets and curly braces are treated as parentheses, so 2*[3+(4-1)] works. Just remember to close each one.
Does the calculator save what I type?
No. The calculation is done in your own browser, and the expression is neither sent nor stored. When you reload the page, the field comes back empty.
Can I use letters like x and y in the expression?
No. The tool calculates numerical values, without variables. The only letters accepted are function names (sin, ln…) and the constants pi, e and phi. To solve equations, use the Quadratic Equation Calculator.
Before you trust the result
This calculator interprets the expression exactly as it was written. If the parentheses are in the wrong place, it calculates the wrong thing without noticing, because it has no way of guessing your intention. Reread the "The expression was read as" line in the step-by-step to check.
Numbers are stored with about 15 significant digits, and the result is shown with at most 10 decimal places, so tiny differences in the last decimal places are to be expected. This tool is for studying, checking exercises and quick reference. Do not use the results as the only basis for financial, medical, legal, structural or safety decisions. In those cases, consult a professional and check the calculation another way. Checking and using the answers is entirely the user's responsibility.
Bottom line: this tool is educational. Results do not replace your own checking, and how you use them is entirely your responsibility. More details in the legal notice.
Where a scientific calculator helps
- School and entrance exams. Functions, logarithms, trigonometry and combinatorics are in almost every math and physics exam. Checking the numerical answer helps you find the error in your reasoning.
- Physics and chemistry. Scientific notation, powers of ten and logarithms show up in waves, circuits, radioactive decay and the calculation of pH.
- Statistics. Factorials and combinations are used for counting and probability, and roots come into standard deviation.
- Personal finance, for study. Compound interest uses powers, and the time for a value to double uses logarithms.
- Trades and workshop projects. Triangles, ramps and cutting angles call for trigonometry, but for measurements that will actually be built, always check another way.
- Programming. When testing a formula before putting it into code, a quick calculation shows the expected result.
Terms you will come across
- Numerical expression
- A set of numbers, operations and parentheses that results in a single value.
- Radian
- An angle unit in which a full turn is 2π. One radian measures about 57.3°.
- Degree
- An angle unit in which a full turn is 360.
- Gradian
- An angle unit in which a full turn is 400 and a right angle is 100.
- Logarithm
- The exponent to which the base must be raised to get a number. If 10³ = 1000, then log 1000 = 3.
- Factorial
- The product of all integers from 1 to n, written n!. For example, 5! = 120.
- Euler's number (e)
- An irrational number, approximately 2.71828, the base of the natural logarithm.
- Scientific notation
- A way of writing numbers as a value between 1 and 10 multiplied by a power of ten.
- Precedence
- The order in which operations are solved: parentheses, functions, powers, multiplication and division, addition and subtraction.
- Floating point
- The format computers use to store decimal numbers, with about 15 to 16 significant digits.
From logarithm tables to your pocket
Before calculators, people doing complex calculations used logarithm tables, the basis of which was published by the Scotsman John Napier in 1614. Logarithms turned difficult multiplications into additions, and the slide rule, which grew out of this principle, was the engineer's tool for more than three centuries.
The pocket scientific calculator arrived in the 1970s. The HP-35, from Hewlett-Packard, launched in 1972, is cited as the first of its kind, with trigonometric functions, logarithms and exponentials in a device that fit in a shirt pocket. Within a few years the slide rule left the stage.
The symbols we use have their own histories. The square root sign appears in print in the 16th century. The letter π for the ratio of a circle's circumference to its diameter was used by William Jones in 1706 and popularized by Leonhard Euler. The exclamation mark for the factorial was proposed by Christian Kramp in 1808, partly to save space in printing.
Numerical curiosities
- 0! = 1. It seems strange, but it is the definition that keeps the combination formulas working.
- The number e (2.71828…) is the limit of (1 + 1/n)ⁿ as n grows. It came from a compound interest problem.
- The golden ratio, φ, is (1 + √5) ÷ 2 ≈ 1.618. Type
phito use it. - π never repeats. Its decimal places neither end nor form a cycle, and the calculator only shows the beginning.
- 100! has 158 digits. That is why this tool's limit is 170!, the last factorial that fits in the numeric format used by computers.
- A full turn has three common measures: 360 degrees, 2π radians or 400 gradians.