Evaluating Expressions Calculator 

Evaluating an expression means working out its value by applying the order of operations correctly: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. This calculator does that three ways. Batch mode evaluates many expressions at once, one per line. Single mode evaluates one expression and shows every step it took. Variables mode substitutes your values for named variables such as x, y and z first, then evaluates with steps.

Supported syntax: + – * / and ^ for powers, parentheses, decimals, negative numbers, the constant pi, and the functions sqrt, abs, round, floor, ceil, sin, cos, tan, log (base 10) and ln (natural log). Trig functions work in radians. The tool evaluates expressions only: it does not solve equations, simplify symbolically or draw graphs, and the sections below state its exact limits, including the places where the three modes behave differently.

Quick Answer

How to use the three modes

Pick a tab, enter your expressions, choose a precision, and press Evaluate. Results stay hidden until you do, and each mode can load its own sample with the Load sample expressions button.

Two honest differences between the modes are worth knowing before you rely on them. Batch mode also accepts ** for powers (3**3 = 27); the step-by-step parser used by Single and Variables mode accepts ^ only, and 3**3 fails there. And when a line or expression fails, the card shows one generic message, "Error: invalid expression", in every mode: the tool does not tell you which character caused the problem, so check parentheses, operators and names first.

The order of operations this calculator follows

Evaluation follows PEMDAS (called BODMAS in some countries), the convention that gives every expression exactly one value. As Mathematics LibreTexts puts it in its order of operations lesson, grouping symbols come first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. The step list in Single mode is that convention made visible: each numbered step is one operation, applied in the order the rules require.

Two details catch people out. First, multiplication and division have equal rank, as do addition and subtraction, so 16 / 4 * 2 is 8 (divide first, because it comes first) and not 2. Second, a minus sign in front of a number or a parenthesis is handled as negation at the point where it appears: the step list shows -(5) = -5 and -(3 + 4) = -7 as their own steps, which is exactly how the parser treats them. If your expression is really a fraction problem rather than a division problem, the fraction addition calculator works in exact fractions instead of decimals.

Supported functions and symbols

Every function takes one value in parentheses and binds more tightly than any operator, so sqrt(169) + 7 evaluates the root before the addition. Angles for sin, cos and tan are in radians, and pi is available as a constant in all three modes.

Watch floor with negatives: floor(-2.5) is -3, not -2, because floor always rounds toward the smaller number. For powers, ^ is the symbol to use everywhere; writing a power in exponential form instead is covered by the convert to exponential form calculator. The % operator does not exist in Single and Variables modes, but Batch mode accepts % as the remainder operator (so a batch line such as 10 % 3 evaluates to 1); there is no factorial, and no square brackets or braces, in any mode: convert [ and { to parentheses before evaluating.

Worked examples, verified against the calculator

Batch. The six pre-filled lines evaluate to the following. Every row is a real run of the tool above, so you can clear the box, type any row back in, and get the same figure.

Single with steps. For 8 * (5 + 3) - 16 / 4 the tool lists: 1) 5 + 3 = 8; 2) 8 * 8 = 64; 3) 16 / 4 = 4; 4) 64 - 4 = 60. Note the order: the parentheses resolve first, then the multiplication and the division in the order the evaluation reaches them, and the subtraction comes last even though it sits in the middle of the written expression.

Variables. With x=2 and y=3, the expression 2*x + 3*y - 4 evaluates in four steps: 2 * 2 = 4, 3 * 3 = 9, 4 + 9 = 13, 13 - 4 = 9. Drop the - 4 and the same definitions give 13 for 2*x + 3*y. Substitution itself is the standard method taught for evaluating expressions with two variables at Khan Academy: replace every occurrence of each variable with its value, in parentheses, then follow the order of operations. Longer names work too, and the tool substitutes the longest name first, so with a=1.5 and ab=10 the expression ab - a correctly gives 8.5 rather than confusing ab with a.

Evaluating expressions vs evaluating a linear function

These two tasks sound alike and are often confused, so the boundary is worth stating. This page evaluates any arithmetic or algebraic expression you type: any operators, any of the ten functions, any variable names, in batches or one at a time. It knows nothing about slope, intercepts or lines.

If your problem is specifically a linear function, f(x) = mx + b, and you want the value at one x together with the intercepts and a table of nearby values, that narrower job belongs to the evaluate linear functions calculator, which takes slope, intercept and x as three separate fields. Use this page when the expression is not in mx + b form, when it uses powers, roots or logs, or when you need many expressions or many variables at once. Neither tool solves for an unknown: both evaluate at values you supply.

Known limits of this tool, stated plainly

• No implicit multiplication outside Batch quirks: 2(3+4) fails in every mode. In Single and Variables mode the parser also rejects 2x: write 2*x.
• ** is Batch-only: Batch mode accepts 3**3; the step parser accepts ^ only.
• One generic error message: a failed line reads "Error: invalid expression" whether the cause is a mismatched parenthesis, division by zero, an unknown name or a bad character. Only the variable definitions get specific messages, such as a reserved name or a missing value.
• Numbers take one decimal point: in Single and Variables mode the parser reads 1.2.3 as 1.2 and carries on, so a doubled decimal point will not warn you. Batch mode rejects it instead.
• Auto precision is raw: floating point artifacts such as 0.1 + 0.2 = 0.30000000000000004 are shown as they are. If you need the answer as an exact fraction afterwards, the decimal to fraction calculator converts the rounded decimal.
• Batch is maths only: lines that are JavaScript rather than maths (for example Math.random(), an assignment, or a line ending in a semicolon) are rejected, even where a browser console would run them.
• No equation solving, no graphing, no units: an equals sign, a request to find x, or attached units are outside what this tool does.

One more disclosure about Batch mode: every line is parsed by a whitelist maths parser, the same approach Single and Variables mode use, and nothing you type is run as JavaScript. Only numbers, the operators + - * / % ^ (or **), parentheses, pi and the named functions are accepted; the Math. forms such as Math.pow(2, 10) and Math.sqrt(9) work as aliases for the same functions. Anything else, including other JavaScript, semicolons, square brackets and unknown names, is rejected as an invalid expression.

What competing calculators miss

The big general solvers are powerful but shaped differently, and the small expression tools each drop something this page keeps.

• Mathway and Symbolab evaluate one problem at a time inside broad solver platforms, and their full step detail sits behind account prompts. Neither offers a plain batch box where thirty homework expressions evaluate in one click with a success count.
• MathPapa is an algebra specialist: strong on solving and factoring equations step by step, but it is built around algebra problems, not around evaluating long lists of plain arithmetic expressions with functions, precision control and copyable results.
• Sage Calculator comes closest, with an algebra expression tool that auto-detects variables and a separate evaluate-each-expression tool for one-per-line input. The two jobs live on two different pages, variable definitions are handled differently on each, and neither shows a per-operation step list for the batch lines.
• iotools Math Evaluator uses the mathjs engine, so it accepts far wider syntax (modulo, units, matrices) and explains per-line errors, but that width is also its risk for a student: it answers questions this page's stricter PEMDAS parser would flag, and it has no dedicated variables mode with named definitions.
• Calculator.now and GEG Calculators cover single-expression evaluation with variables, but stop at the answer: no batch mode, no precision selector, and no copy or share of a result set.

The gap this page fills is the combination: batch evaluation, a visible step list, named variable substitution, fixed or exact precision, and copy/share on the results, with its syntax limits stated on the page instead of discovered by trial and error.

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