About This Tool
A scientific calculator handles the full range of mathematical operations that a basic four-function calculator cannot: trigonometric functions, logarithms, exponents, roots, and constants like pi and Euler's number. This free scientific calculator goes beyond button-mashing by accepting typed expressions such as "sqrt(144) + sin(pi/2) * 3^2", parsing them with proper operator precedence, and returning an exact result. You can switch between degree and radian modes for trigonometric functions, review your last five calculations in the built-in history panel, and quickly insert common functions using the shortcut buttons. The expression parser supports nested parentheses, unary negation, and right-associative exponentiation, so complex formulas like "2^3^2" correctly evaluate to 512 rather than 64. If you make a syntax error or attempt an impossible operation like dividing by zero, the calculator provides a clear error message instead of a cryptic NaN. All of your data stays private and nothing is stored or shared.
Operator Precedence and Evaluation Order
Mathematical expressions follow a strict order of operations. This calculator implements the standard precedence rules used in mathematics and most programming languages:
- Parentheses are evaluated first and can override any precedence rule.
- Functions like sin(), cos(), sqrt() are evaluated next.
- Unary operators (negative sign) bind tightly: -3^2 evaluates as (-3)^2 = 9.
- Exponentiation (^) is right-associative: 2^3^2 means 2^(3^2) = 2^9 = 512.
- Multiplication and Division are evaluated left to right.
- Addition and Subtraction are evaluated last, left to right.
This means an expression like "2 + 3 * 4" returns 14 (not 20), because multiplication happens before addition. To force addition first, use parentheses: "(2 + 3) * 4" returns 20.
Trigonometric Functions and Angle Modes
Trigonometric functions are fundamental to physics, engineering, and geometry. This calculator supports six trigonometric functions:
- sin(x) returns the sine of angle x.
- cos(x) returns the cosine of angle x.
- tan(x) returns the tangent of angle x. Undefined at 90 and 270 degrees (pi/2 and 3pi/2 radians).
- asin(x) returns the arc sine (inverse sine). Input must be between -1 and 1.
- acos(x) returns the arc cosine (inverse cosine). Input must be between -1 and 1.
- atan(x) returns the arc tangent (inverse tangent).
Degree vs. Radian mode: Radians are the mathematical standard where a full circle is 2*pi (approximately 6.2832). Degrees divide a circle into 360 equal parts. Use the mode selector to choose which unit your angles are in. For example, sin(90) in degree mode returns 1, while sin(pi/2) in radian mode also returns 1.
Logarithms and Exponential Functions
Logarithms answer the question "to what power must I raise a base to get this number?" This calculator supports two types:
- log(x) computes the base-10 (common) logarithm. log(100) = 2 because 10^2 = 100.
- ln(x) computes the natural logarithm (base e, where e is approximately 2.71828). ln(e) = 1 because e^1 = e.
Both functions require a positive input. Logarithm of zero or a negative number is undefined and will show an error message.
Related exponential operations:
- e^x can be typed as "e^x" or "exp(x)". For example, exp(1) returns 2.71828.
- 10^x is typed directly as "10^x". For example, 10^3 returns 1000.
- Arbitrary powers use the caret operator: 2^10 returns 1024.
Constants and Special Values
Two mathematical constants are built into the calculator and can be used directly in expressions:
- pi (approximately 3.14159265358979) represents the ratio of a circle's circumference to its diameter. Common uses: area of a circle (pi * r^2), converting degrees to radians (degrees * pi / 180).
- e (approximately 2.71828182845905) is Euler's number, the base of the natural logarithm. It appears in compound interest formulas, probability distributions, and exponential growth models.
Examples using constants:
- Area of a circle with radius 5:
pi * 5^2returns 78.5398... - Compound interest factor:
e^0.05returns 1.05127... (about 5.13% growth) - Half a circle in radians:
pi / 2returns 1.5707...
Error Handling and Edge Cases
The calculator provides descriptive error messages for invalid operations instead of returning confusing results:
- Division by zero: Expressions like "5/0" display "Division by zero" instead of Infinity.
- Square root of negative numbers: "sqrt(-4)" shows an error. For complex number math, use the formula manually: sqrt(4) * i.
- Log of non-positive numbers: "log(0)" and "log(-5)" both show clear error messages since logarithms are only defined for positive real numbers.
- Mismatched parentheses: "sin(45" triggers a syntax error prompting you to close the parenthesis.
- Unknown functions: Typing "sine(45)" instead of "sin(45)" returns "Unknown function: sine" so you know to correct the name.
- Factorial overflow: "factorial(171)" exceeds the maximum representable value. The calculator supports factorials up to 170.
If you see an unexpected error, check for typos, mismatched parentheses, or missing multiplication signs. Note that implicit multiplication (like "2pi") is not supported; use "2*pi" instead.
Frequently Asked Questions
How do I calculate powers and roots?
Use the caret operator (^) for powers. For example:
2^8calculates 2 to the 8th power (256).5^0.5calculates the square root of 5 (same as sqrt(5)).27^(1/3)calculates the cube root of 27 (3).
For square roots specifically, you can also use the sqrt() function: sqrt(144) returns 12.
What is the difference between log and ln?
log(x) computes the base-10 logarithm. It answers "10 raised to what power equals x?" For example, log(1000) = 3 because 10^3 = 1000.
ln(x) computes the natural logarithm (base e). It answers "e raised to what power equals x?" For example, ln(e) = 1 because e^1 = e.
Base-10 logs are common in chemistry (pH scale), acoustics (decibels), and earthquake measurement (Richter scale). Natural logs appear in calculus, compound interest, and population growth models.
When should I use degrees versus radians?
Use degrees when working with everyday angles: navigation, construction, geometry homework, or compass bearings. A right angle is 90 degrees, a straight line is 180 degrees, and a full rotation is 360 degrees.
Use radians when working with calculus, physics, or advanced mathematics. A right angle is pi/2 radians, a straight line is pi radians, and a full rotation is 2*pi radians. Most mathematical formulas and scientific papers assume radian measure.
To convert: degrees = radians * 180 / pi. Radians = degrees * pi / 180.
Does this calculator support implicit multiplication?
No. You must use the * operator explicitly. For example:
- Write
2 * piinstead of2pi. - Write
3 * sin(45)instead of3sin(45). - Write
(2 + 3) * (4 + 5)instead of(2 + 3)(4 + 5).
This requirement avoids ambiguity. In some notations, "xy" could mean "x times y" or a variable named "xy". Explicit multiplication removes that confusion.
What is the maximum number this calculator can handle?
The calculator uses standard floating-point arithmetic, which supports numbers up to approximately 1.8 x 10^308 and as small as 5 x 10^-324. For extremely large or small results, the output switches to scientific notation (e.g., "1.5e+20").
Precision is limited to about 15-17 significant digits. This means very large integers may lose precision in their last few digits. For example, 2^53 + 1 and 2^53 produce the same result due to floating-point limitations. For most practical calculations, this level of precision is more than sufficient.
How does exponentiation associativity work?
Exponentiation in this calculator is right-associative, which matches mathematical convention. This means 2^3^2 is evaluated as 2^(3^2) = 2^9 = 512, not as (2^3)^2 = 8^2 = 64.
If you need left-to-right evaluation, use parentheses explicitly: (2^3)^2 gives 64. Right-associativity is the standard in mathematics because it produces more useful results: repeated exponentiation builds "towers of powers" from the top down.