Scientific Calculator
A scientific calculator reads the whole expression first, so 2 + 3 x 4 is 14 while (2 + 3) x 4 is 20. It handles powers, roots, logs, factorials and angles in degrees or radians, and 1.05^10 comes back as 1.628895.
Type a full expression the way it is written on paper, then press Enter. Use ^ for powers, ! for factorials, and pi or e for the constants. Everything runs in your browser.
| Result | |
| Rounded to 6 significant figures | |
| Scientific notation | |
| Expression as read |
All calculations run in your browser, and nothing you type is uploaded or stored.
Type a full expression with powers, roots, logs, trig and factorials. The calculator applies the order of operations and shows the answer at full, rounded and scientific precision.
Key takeaways
- Order of operations: parentheses, then powers, then multiply and divide, then add and subtract
- Powers run right to left, so 2^3^2 is 512, not 64
- Angles default to degrees: sin(30) is 0.5, but in radians it is -0.988032
- Factorials stop at 170! because 171! overflows the number format
On this page
What makes a calculator scientific
A basic calculator works left to right. A scientific one reads the whole expression first, applies the order of operations, and only then returns a number. That single difference is why the same keystrokes give different answers: on a basic calculator 2 + 3 x 4 comes out as 20, and on a scientific calculator it comes out as 14.
This page is the second kind. You type an expression the way it is written on paper, press Enter, and it evaluates powers before multiplication, multiplication before addition, and parentheses before everything. It also carries the functions that turn a four function machine into a useful one: square roots, logarithms, sines and cosines, factorials and the two constants pi and e.
| Key or symbol | What it does | Example |
|---|---|---|
| ^ | Raises a number to a power | 2^10 = 1024 |
| sqrt | Square root | sqrt(2) = 1.414214 |
| ! | Factorial, the product of every whole number up to it | 5! = 120 |
| ln | Natural log, base e | ln(1000) = 6.907755 |
| log | Common log, base 10 | log(1000) = 3 |
| sin, cos, tan | Trig ratios, in degrees or radians | sin(30) = 0.5 in degrees |
| pi, e | Constants, 3.141593 and 2.718282 | 2pi = 6.283185 |
There is no percent key. A percentage is a division by 100, so 15 percent of 240 is written 240 x 0.15, and the answer is 36.
Order of operations, and why 2 + 3 x 4 is 14
The rules are the ones from school, applied without exception. Parentheses first, then powers and roots, then multiplication and division, then addition and subtraction. Operations at the same level run left to right, with one exception: a stack of powers runs right to left.
| Level | Operations | How it reads |
|---|---|---|
| 1 | Parentheses and function arguments | (2 + 3) x 4 = 20 |
| 2 | Powers and factorials | 2^10 = 1024 |
| 3 | Multiplication and division, left to right | 8 / 2 / 2 = 2 |
| 4 | Addition and subtraction, left to right | 10 - 4 - 3 = 3 |
Unary minus binds looser than a power, which matches the usual convention: -2^2 is -4, not 4, because the power is applied to 2 and then the sign is applied. Write (-2)^2 if you want 4.
Powers associate to the right, so 2^3^2 is 2^(3^2) = 2^9 = 512, not (2^3)^2 = 64. Spreadsheets and most programming languages do the same, so the habit carries over.
Two habits prevent most order of operations errors. Put every subtraction that might be confused for a negative number in parentheses, and put a fraction like 1 / (2 + 3) in parentheses on the bottom, because 1 / 2 + 3 is 3.5 while 1 / (2 + 3) is 0.2.
Degrees versus radians
Every trigonometry function needs to know how the angle is measured. A full circle is 360 degrees or 2 pi radians, so one radian is 180 / pi = 57.2958 degrees, and a right angle is 1.570796 radians.
This trips people up because the wrong setting does not produce an error, it produces a plausible looking number. sin(30) with the calculator in degrees is 0.5. Switch to radians and the same keys give -0.988032, because 30 radians is 30 / 6.283185 = 4.774 full circles plus a bit, and that bit lands in the fourth quadrant where the sine is negative and close to minus one.
| Angle | Degrees | Radians | Sine |
|---|---|---|---|
| One twelfth of a turn | 30 | 0.523599 | 0.5 |
| One eighth of a turn | 45 | 0.785398 | 0.707107 |
| One sixth of a turn | 60 | 1.047198 | 0.866025 |
| Right angle | 90 | 1.570796 | 1 |
| Straight line | 180 | 3.141593 | 0 |
The inverse functions return the angle in whichever unit is selected. asin(0.5) gives 30 in degrees and 0.523599 in radians, which is a quick way to check that the setting matches what you expect.
Radians are the default in calculus and in most programming languages. Degrees are the default in construction, navigation and anything measured with a protractor. Pick by the source of the number, not by habit.
Logs: log, ln and log2
Three log keys, three bases, one idea. A logarithm answers the question: what power do I raise the base to in order to get this number?
log(1000) is 3 because 10^3 = 1000. ln(1000) is 6.907755 because e raised to that power is 1000, and e is 2.718282. log2(1024) is 10 because 2^10 = 1024, which is why storage sizes and doubling times use base 2.
Any log can be rewritten in another base by dividing: log base b of x equals ln(x) / ln(b). That is exactly how this calculator computes log and log2, since JavaScript only ships the natural log. OpenStax's college algebra chapter on logarithms covers the change of base rule and the domain restrictions.
Two rules of thumb are worth keeping. A log of a number between 0 and 1 is negative, so ln(0.5) is -0.693147. And a log of zero or of a negative number is not defined for real numbers, so the calculator refuses instead of returning a fake answer.
Logs turn multiplication into addition, which is why they show up in compound growth. Doubling time at a steady rate r is ln(2) / ln(1 + r), and at 8 percent that is 9.01 years.
Powers, roots and factorials
A power is repeated multiplication: 1.05^10 means 1.05 multiplied by itself ten times, which is 1.628895. That single expression is the whole idea behind compound interest, and it is the most common reason people reach for a scientific calculator.
A fractional power is a root. 2^0.5 and sqrt(2) both give 1.414214, and 8^(1/3) gives 2. A negative power is a reciprocal, so 2^-3 is 0.125.
Factorials grow faster than most people expect. 5! is 120, 10! is 3,628,800, and 69! is about 1.71 x 10^98, which is already past the number of atoms in a small object. The usual double precision limit arrives at 170!, which is about 7.26 x 10^306. One more and the result overflows, so this calculator stops at 170 and tells you why instead of printing infinity.
Factorials only accept whole numbers. 5.5! has a meaning in advanced math through the gamma function, but not on a calculator keypad, so the tool rejects it rather than guessing.
Scientific notation without losing digits
Calculators write very large and very small numbers with an exponent. The number 6.02 x 10^23 is typed as 6.02e23, and multiplying it by 2 gives 1.204e24. The e is not Euler's constant here, it is shorthand for times ten to the power of.
This calculator accepts both forms. Typing 6.02e23 and 6.02*10^23 returns the same value, and the result panel shows the answer three ways: full precision, rounded to six significant figures, and in scientific notation. The three views are the same number, so a discrepancy between them means the value sits close to a rounding boundary.
Scientific notation is also the honest way to report a measurement. A length written as 6.02e23 has three significant figures, and claiming 6.020000e23 implies a precision that no instrument delivers. NIST Special Publication 811 is the reference for how many digits to keep and where to round when units are involved.
Rounding should happen once, at the end. Rounding after each step is how a chain of small errors becomes a wrong answer, especially in unit conversions where factors like 25.4 and 0.9144 are exact but intermediate decimals are not.
Why 0.1 + 0.2 does not show 0.30000000000000004
Computers store decimals in binary, and most decimal fractions have no exact binary form. One tenth is one of them. The stored value of 0.1 is slightly more than 0.1, the stored value of 0.2 is slightly more than 0.2, and adding them gives a number whose last bits are off.
The exact sum in double precision is 0.30000000000000004. This calculator displays 12 significant figures and trims the trailing zeros, so you see 0.3. That is not the calculator hiding an error, it is the honest display of a value that is correct to the precision anyone needs for a measurement or a price.
The same effect shows up in money when you multiply by percentages. 0.07 x 100 can land on 7.000000000000001, which rounds to 7.000000000000 at 12 digits and displays as 7.
Where it matters is comparison. Two values that should be equal can differ in the last bit, so tests for equality in spreadsheets and code need a tolerance rather than an exact match. For homework, a price or a length, the display precision is far beyond what the input deserves.
Reading the answer without fooling yourself
A calculator returns as many digits as it can, and most of them are not real. The rule that keeps you honest is to carry the input's precision through the work and round once at the end.
If you measure a room as 12.5 feet by 9.25 feet, you have three significant figures in the first number and three in the second. The area is 115.625 square feet on screen, and 116 square feet is the defensible answer. Quoting 115.625 claims a precision of a thousandth of a square foot from a tape measure that reads to an eighth of an inch.
Angles deserve the same treatment. A half degree of error over 20 feet moves the far end by about 2 inches, so reporting an angle to four decimals when the instrument reads to one degree is decoration, not information.
The last check is a sanity pass. sin(30) should be 0.5, not -0.988. sqrt(2) should be a little above 1.4. 1.05^10 should be a little above 1.6, because 5 percent for 10 years is more than 50 percent. If an answer fails one of those checks, the input or the angle mode is wrong, not the arithmetic.
Frequently asked questions
Why does 2 + 3 x 4 give 14 and not 20?
Because multiplication runs before addition. 3 x 4 is 12, and 12 + 2 is 14. A basic calculator that works left to right would give 20, which is why the order of operations matters.
How do I enter a negative exponent?
Type a minus sign inside the power: 2^-3 gives 0.125. A leading minus on the whole expression binds after the power, so -2^3 is -8 and (-2)^3 is also -8, but -2^2 is -4 while (-2)^2 is 4.
How do I take a cube root?
Use a fractional power. 27^(1/3) gives 3, and 8^(1/3) gives 2. The sqrt key is only for square roots.
Why is sin(30) negative on my calculator?
The angle mode is set to radians. 30 radians is 4.77 full turns, which lands in the fourth quadrant, so the sine is -0.988032. Switch to degrees and sin(30) is 0.5.
What is the difference between log and ln?
log is base 10, ln is base e. log(1000) is 3 and ln(1000) is 6.907755. Both answer the same question with a different base.
How many digits does the calculator keep?
It displays 12 significant figures and trims trailing zeros, which is close to the 15 to 17 digits that double precision holds internally. Rounding for the final answer is your choice, not the calculator's.
Why does 0.1 + 0.2 show 0.3 instead of 0.30000000000000004?
The stored sum is 0.30000000000000004, and the display keeps 12 significant figures, so it rounds to 0.3. The tiny difference comes from binary storage, not from the arithmetic.
What is 15 percent of 240?
36. There is no percent key, so type 240 x 0.15. A percentage is the number divided by 100, so 15 percent is 0.15.
How large a factorial can this handle?
Up to 170!. 170! is about 7.26 x 10^306 and 171! overflows the number format, so the calculator stops there with a message instead of returning infinity.
What does 1.05^10 mean in money terms?
It is the growth factor for 5 percent a year over 10 years, 1.628895. A $1,000 balance becomes $1,628.90 if the rate compounds once a year.
Can I type numbers with commas?
Yes. 1,000 + 500 is read as 1,500, because commas between digits are treated as thousands separators and removed before the expression is evaluated.
How do I compute log base 5 of 25?
Divide the logs: ln(25) / ln(5) = 2. Any base works that way, and the calculator evaluates the division directly.
Why does my answer differ in the last digit from another calculator?
Different tools round at different points and store a different number of bits. A difference in the last displayed digit is normal; a difference in the first three digits means one of the inputs or the angle mode is wrong.
What does 2^3^2 equal?
512. Powers run right to left, so 3^2 is 9 first and 2^9 is 512. Writing (2^3)^2 would give 64 instead.
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