Scientific Calculator

Evaluating a Full Math Expression with Order of Operations

A scientific calculator evaluates a full math expression — not just one operation at a time — following the standard order of operations. Type an expression using the field or the button pad below, including parentheses, trig functions, logarithms, exponents, and factorials, and get the result instantly.

Unlike a basic four-function calculator, this one understands an entire expression at once, the same way a graphing calculator or a math textbook does: 3 + 4 * 2 correctly evaluates to 11 (not 14), because multiplication happens before addition, and sqrt(16) + 2^3 correctly evaluates to 12, combining a function call with an exponent in the same expression.

The Formula

Expressions are evaluated in this order, from first to last:

1. Parentheses and function calls — anything inside ( ), including a function’s own argument (like the 16 inside sqrt(16)), is evaluated first.
2. Exponents (^) and postfix operators (! for factorial, % for percent) — evaluated right-to-left for chained exponents ($2^{3^2}$ means $2^{\left(3^2\right)}$, not $\left(2^3\right)^2$).
3. Multiplication and division (*, /), left-to-right.
4. Addition and subtraction (+, -), left-to-right.

The Degrees / Radians setting controls how the trig functions (sin, cos, tan, and their inverses) interpret angles — the same expression means something different in each mode, so pick whichever matches the problem at hand.

Worked Example

Evaluating $\sqrt{16} + 2^3$:

1. Evaluate the square root first: $\sqrt{16} = 4$. 2. Evaluate the exponent: $2^3 = 8$. 3. Add the two results together: $4 + 8 = 12$.

Functions and exponents are resolved first (steps 1 and 2), and only then are the two results added together (step 3) — evaluating strictly left-to-right without following this order would give a different, incorrect answer.

Key Factors to Consider

• Mixing up Degrees and Radians mode is one of the most common sources of a wrong trig result. The same expression, like sin(90), gives a completely different answer depending on whether 90 is interpreted as 90 degrees (giving 1) or 90 radians (a value that’s not even close to a recognizable landmark angle) — always confirm which mode is active before trusting a trig result.
• Implicit multiplication (like 2(3+4) or 3pi) is a convenience this calculator supports, but it’s worth understanding it’s still standard multiplication under the hood. Writing a number directly next to a parenthesis or a named constant is a common shorthand in math notation — this calculator interprets it exactly the same as if a * were written explicitly.
• A missing or mismatched parenthesis is one of the most common typing errors when entering a complex expression. Since every function call and grouped sub-expression needs its own matching close-parenthesis, a long expression with several nested functions is worth double- checking for balanced parentheses before assuming an unexpected result is a calculation error rather than a typo.
• This calculator never uses eval() or similar direct code-execution shortcuts, for a real security reason. Running a string a user typed directly as executable code is a well-known security risk for any tool that accepts free-text math input — this calculator instead parses the expression as pure data using a proper mathematical grammar, the same safe approach any well-built calculator application should use.

Common Mistakes

• Forgetting that ^ is right-associative for chained exponents. 2^3^2 means $2^{\left(3^2\right)} = 512$, not $\left(2^3\right)^2 = 64$ — the rightmost exponent resolves first, the opposite of how left-to-right operators like + and * work.
• Assuming a negative sign always applies before an exponent. -2^2 evaluates to -4, not 4, since the exponent binds to the 2 before the unary minus is applied — use explicit parentheses, like (-2)^2, when you actually want the negative number squared.
• Not checking which angle mode is active before reading a trig result. A perfectly correctly typed expression like sin(90) gives a completely different, equally “correct” answer in Degrees mode versus Radians mode — the calculator isn’t wrong, the assumed mode was.

Useful to Know

• Need to solve a quadratic equation rather than just evaluate one expression? Quadratic Formula Calculator handles that directly, including complex roots.
• Working with very large or very small numbers in scientific notation? Scientific Notation Calculator converts between standard and scientific notation.
• Need a simpler four-function calculator without the scientific functions? Basic Calculator covers everyday arithmetic without the extra complexity.