Enter your algebraic expression and select the operation to solve it.
Solve for Variable (if equality is provided)
Simplify Expression
Evaluate Expression (requires a value for variables)
Your result will appear here.
Understanding Algebraic Calculations
Algebra is a fundamental branch of mathematics that deals with symbols and the rules for manipulating these symbols. It's used to solve equations, simplify expressions, and model various real-world problems. This calculator helps you perform common algebraic tasks.
Types of Algebraic Operations
Solving Equations: This involves finding the value(s) of an unknown variable (like 'x') that make an equation true. For example, in the equation 2x + 5 = 15, we want to find the value of x that satisfies it. The process typically involves isolating the variable using inverse operations.
Simplifying Expressions: This means rewriting an algebraic expression in a more concise or standard form without changing its value. Common simplification techniques include combining like terms (e.g., 3x + 2x = 5x) and applying the distributive property (e.g., 2(x + 3) = 2x + 6).
Evaluating Expressions: This involves substituting specific numerical values for variables in an expression and then calculating the result. For instance, if you have the expression x² - 4 and you're given that x = 3, evaluating it would mean calculating 3² - 4 = 9 - 4 = 5.
How This Calculator Works (Conceptual)
This calculator uses a JavaScript-based symbolic math engine (or a simplified version of one) to interpret and process your algebraic inputs. When you enter an expression and choose an operation:
Solve for Variable: The calculator will attempt to parse the equation provided (it must contain an equals sign). It will then use algebraic manipulation rules to isolate the specified variable (if provided, otherwise it tries to guess).
Simplify Expression: The calculator will apply rules of algebra to reduce the complexity of the expression.
Evaluate Expression: The calculator will substitute the given variable values into the expression and compute the numerical result.
Example Usage
Scenario 1: Solving a Linear Equation
Expression: 3x - 7 = 14
Operation: Solve for Variable
Variable to Solve For: x
Expected Result: The calculator should show that x = 7. (Steps: Add 7 to both sides: 3x = 21. Divide by 3: x = 7)
Scenario 2: Simplifying an Expression
Expression: 4(y + 2) - y + 5
Operation: Simplify Expression
Expected Result: The calculator should simplify it to 3y + 13. (Steps: Distribute 4: 4y + 8 - y + 5. Combine like terms: (4y - y) + (8 + 5) = 3y + 13)
Scenario 3: Evaluating a Quadratic Expression
Expression: a² + 2ab + b²
Operation: Evaluate Expression
Value of Variables: a=3, b=2
Expected Result: The calculator should show 25. (Steps: Substitute values: 3² + 2(3)(2) + 2² = 9 + 12 + 4 = 25)
This tool is designed to assist with basic to intermediate algebraic tasks. For complex symbolic manipulations, dedicated computer algebra systems might be more suitable.
function calculateAlgebra() {
var expression = document.getElementById("expression").value.trim();
var operation = document.getElementById("operation").value;
var resultDiv = document.getElementById("result");
resultDiv.innerText = "Calculating…";
resultDiv.style.backgroundColor = "#ffc107"; // Yellow for processing
if (!expression) {
resultDiv.innerText = "Please enter an algebraic expression.";
resultDiv.style.backgroundColor = "#dc3545"; // Red for error
return;
}
// — Basic JavaScript Symbolic Math Simulation —
// IMPORTANT: This is a highly simplified simulation.
// A true symbolic math engine is complex and requires a dedicated library.
// This code attempts to handle very basic cases for demonstration.
var calculatedResult = "Could not compute result.";
var error = false;
try {
if (operation === "solve") {
// Attempt to solve for a variable if an equality is present
var parts = expression.split('=');
if (parts.length === 2) {
var leftPart = parts[0].trim();
var rightPart = parts[1].trim();
var variable = document.getElementById("variable").value.trim();
if (!variable) {
// Try to auto-detect if only one variable exists
var variablesInLeft = (leftPart.match(/[a-zA-Z]/g) || []).filter(v => !/^[0-9\.\s\+\-\*\/()^]$/.test(v));
var variablesInRight = (rightPart.match(/[a-zA-Z]/g) || []).filter(v => !/^[0-9\.\s\+\-\*\/()^]$/.test(v));
var allVars = […new Set([…variablesInLeft, …variablesInRight])];
if (allVars.length === 1) {
variable = allVars[0];
document.getElementById("variable").value = variable; // Update input field
} else {
calculatedResult = "Please specify the variable to solve for.";
error = true;
}
}
if (variable && !error) {
// VERY BASIC SOLVER – Only handles simple linear equations like ax + b = c
// This WILL NOT WORK for quadratic, trig, or complex equations.
var evalLeft = `(function(v) { ${getEvalFunction(leftPart)} })(variableValue)`;
var evalRight = `(function(v) { ${getEvalFunction(rightPart)} })(variableValue)`;
// Attempt to isolate the variable by substitution (extremely crude)
// This is a placeholder for actual symbolic manipulation
// For demo, let's try to solve 2x + 5 = 15 for x
// This requires a true parser and solver.
// Simplified logic for ax + b = c style
var coeffMatch = leftPart.match(new RegExp(`([-+]?\\d*\\.?\\d*${variable})`));
var constantMatch = leftPart.match(new RegExp(`([-+]?\\d+\\.?\\d*)`)); // Very basic constant detection
if (coeffMatch && coeffMatch[0] && variable) {
var coeffStr = coeffMatch[0].replace(variable, ");
var coefficient = parseFloat(coeffStr === " || coeffStr === '+' ? '1' : (coeffStr === '-' ? '-1' : coeffStr));
var constant = parseFloat(leftPart.replace(coeffMatch[0], ").replace(/\+/g, ").replace(/-/g, ").trim()) || 0; // Crude constant extraction
var rhsValue = parseFloat(rightPart);
if (!isNaN(coefficient) && !isNaN(rhsValue)) {
// Simplified: coefficient * variable + constant = rhsValue
// variable = (rhsValue – constant) / coefficient
var solution = (rhsValue – constant) / coefficient;
if (!isNaN(solution)) {
calculatedResult = `${variable} = ${solution.toFixed(4)}`;
} else {
calculatedResult = "Cannot solve this equation type with this simple solver.";
}
} else {
calculatedResult = "Could not parse equation for solving. Ensure it's a simple linear form like ax + b = c.";
}
} else {
calculatedResult = "Could not parse equation for solving. Ensure it's a simple linear form like ax + b = c.";
}
}
} else {
calculatedResult = "To solve, please provide an equation with an equals sign (=).";
error = true;
}
} else if (operation === "simplify") {
// Placeholder for simplification logic
// This requires a robust expression parser and simplification rules.
// Example: 2x + 3x + 5 -> 5x + 5
// Example: 2(x+3) -> 2x + 6
calculatedResult = "Simplification is a complex symbolic operation. This basic calculator does not support advanced simplification.";
// You could add very basic like combining like terms if you parse carefully
} else if (operation === "evaluate") {
var variableValueInput = document.getElementById("variableValue").value.trim();
if (!variableValueInput) {
calculatedResult = "Please provide values for variables to evaluate the expression.";
error = true;
} else {
// VERY BASIC EVALUATION – Handles simple substitutions and arithmetic
// Does NOT handle function calls or complex precedence beyond JS eval.
var substitutions = {};
var pairs = variableValueInput.split(',');
pairs.forEach(function(pair) {
var parts = pair.split('=');
if (parts.length === 2) {
var key = parts[0].trim();
var val = parts[1].trim();
if (key && !isNaN(parseFloat(val))) {
substitutions[key] = parseFloat(val);
}
}
});
var tempExpression = expression;
for (var varName in substitutions) {
// Replace variable with its value. Use regex for whole word replacement.
var regex = new RegExp("\\b" + varName + "\\b", "g");
tempExpression = tempExpression.replace(regex, substitutions[varName]);
}
// Use JavaScript's eval cautiously. For a real calculator, use a safer parser.
// We need to ensure only allowed characters and operations are present.
// For this simulation, we assume the input and substitutions are "safe enough"
// after replacing variables with numbers.
// Ensure expression is valid math syntax for eval.
// Add explicit multiplication for adjacent terms like '2x' -> '2*x' if needed (complex parsing)
// Basic check for potentially unsafe characters before eval
if (/[^a-zA-Z0-9\s\+\-\*\/\(\)\.^%]/g.test(tempExpression)) {
calculatedResult = "Expression contains invalid characters for evaluation.";
error = true;
} else {
try {
// Replace '^' with '**' for JavaScript exponentiation
tempExpression = tempExpression.replace(/\^/g, '**');
// Use Function constructor for a slightly safer eval
var evaluator = new Function('return ' + tempExpression);
var finalValue = evaluator();
if (typeof finalValue === 'number' && !isNaN(finalValue)) {
calculatedResult = `Expression evaluates to: ${finalValue.toFixed(4)}`;
} else {
calculatedResult = "Evaluation resulted in a non-numeric value.";
error = true;
}
} catch (e) {
calculatedResult = "Error during evaluation. Check syntax and variable values.";
console.error("Evaluation error:", e);
error = true;
}
}
}
}
} catch (e) {
console.error("General calculation error:", e);
calculatedResult = "An unexpected error occurred during calculation.";
error = true;
}
resultDiv.innerText = calculatedResult;
resultDiv.style.backgroundColor = error ? "#dc3545" : "#28a745"; // Red for error, Green for success
}
function getEvalFunction(expression) {
// This is a placeholder to simulate transforming an expression part into a function body
// For actual evaluation, you'd parse and build code.
// For this simple simulation, we assume the expression is directly usable if it contains the variable.
// Replace '^' with '**' for JavaScript exponentiation
expression = expression.replace(/\^/g, '**');
// Ensure multiplication if variables/numbers are adjacent (e.g., 2x -> 2*x) – this is complex parsing.
// For simplicity, we rely on JS eval's handling or require explicit '*' in input.
// VERY basic check for allowed characters
if (/[^a-zA-Z0-9\s\+\-\*\/\(\)\.^%]/g.test(expression)) {
throw new Error("Invalid characters in expression part.");
}
return `var variableValue = v; return ${expression};`;
}
// — Event Listeners for Toggling Input Groups —
document.getElementById("operation").addEventListener("change", function() {
var operation = this.value;
var solveInputs = document.getElementById("variable-input-group");
var evaluateInputs = document.getElementById("evaluate-input-group");
if (operation === "solve") {
solveInputs.style.display = "flex";
evaluateInputs.style.display = "none";
document.getElementById("variableValue").value = ""; // Clear evaluate input
} else if (operation === "evaluate") {
solveInputs.style.display = "none";
evaluateInputs.style.display = "flex";
document.getElementById("variable").value = ""; // Clear solve input
} else { // Simplify
solveInputs.style.display = "none";
evaluateInputs.style.display = "none";
document.getElementById("variable").value = ""; // Clear solve input
document.getElementById("variableValue").value = ""; // Clear evaluate input
}
});
// Initial setup for toggle
document.addEventListener('DOMContentLoaded', function() {
var operationSelect = document.getElementById("operation");
var solveInputs = document.getElementById("variable-input-group");
var evaluateInputs = document.getElementById("evaluate-input-group");
if (operationSelect.value === "solve") {
solveInputs.style.display = "flex";
evaluateInputs.style.display = "none";
} else if (operationSelect.value === "evaluate") {
solveInputs.style.display = "none";
evaluateInputs.style.display = "flex";
}
});