Complex Expression Evaluator Form
Supported operators and functions
Operators: +, -, *, /, %, ^, parentheses, unary minus, and unary plus.
Functions: sin, cos, tan, asin, acos, atan, sqrt, abs, log, ln, exp, floor, ceil, and round. Constants: pi and e.
Example Data Table
| Expression | X | Y | Z | Angle Mode | Expected Result |
|---|---|---|---|---|---|
| (2+3)^2 - sqrt(16) | 0 | 0 | 0 | Radians | 21 |
| sin(30) + log(100) | 0 | 0 | 0 | Degrees | 2.5 |
| x^3 - 4*x + y | 2 | 1 | 0 | Radians | 1 |
| exp(1) + abs(-5) | 0 | 0 | 0 | Radians | 7.718282 |
| (x+y)/(z+1) | 6 | 4 | 1 | Radians | 5 |
Formula Used
This calculator follows standard operator precedence. Parentheses resolve first, then unary signs, powers, multiplication and division, and finally addition and subtraction.
The expression is converted into Reverse Polish Notation using the shunting-yard method. That step removes ambiguity and makes evaluation reliable for nested operations.
For trigonometric work, the calculator uses: radians = degrees × π / 180 and degrees = radians × 180 / π.
For graphing, it repeatedly evaluates y = f(x) across the chosen x-range while keeping the entered y and z values fixed.
How to Use This Calculator
- Enter your mathematical expression using variables, constants, operators, and supported functions.
- Provide values for x, y, and z if your expression references them.
- Choose radians or degrees for trigonometric evaluation.
- Set the precision level to control decimal output.
- Enter graph start, end, and step values for x.
- Press Evaluate Expression to display the result above the form.
- Review the normalized expression, token stream, RPN output, and Plotly graph.
- Export your session history to CSV or save the visible report as PDF.
Frequently Asked Questions
1. What input style does this evaluator support?
It supports explicit arithmetic syntax with parentheses, variables x y z, constants pi and e, powers, modulo, and common scientific functions. Use explicit multiplication such as 3*x or 2*(x+y).
2. Does it follow the normal order of operations?
Yes. Parentheses are resolved first, then unary signs, powers, multiplication and division, and then addition and subtraction. The parser converts the expression into RPN before calculating the final value.
3. Can I work in degrees for trigonometric expressions?
Yes. Select degrees in the angle mode field before submitting the form. The calculator converts trig inputs and inverse trig outputs so expressions match the selected angle system.
4. Why are some graph points missing?
Missing points usually happen when part of the chosen range causes domain errors, such as dividing by zero or taking a square root of a negative number. Invalid points are skipped automatically.
5. Does it support implicit multiplication like 2x?
No. Use explicit multiplication for dependable parsing. Write 2*x, x*(y+1), or 3*sin(x) instead of 2x, x(y+1), or 3sin(x). This keeps the evaluator clear and consistent.
6. What is Reverse Polish Notation in the results?
Reverse Polish Notation is a postfix version of your expression. It places operators after their operands, which allows the evaluator to compute expressions accurately using a simple stack-based method.
7. What do the CSV and PDF exports include?
The CSV export downloads your recent session history with timestamps, expressions, variables, settings, and results. The PDF export saves the current visible report and can include recent history.
8. How accurate are the results?
Results use floating-point math, so they are suitable for most educational, technical, and analytical work. You can raise the displayed decimal precision, but tiny rounding differences may still appear.