This calculator demonstrates step-by-step calculations for common arithmetic and algebraic operations. Enter your numbers and choose an operation.
Addition (+)
Subtraction (-)
Multiplication (*)
Division (/)
Exponentiation (^)
Square Root (of First Number)
Percentage (%)
Average (Mean)
Understanding the Show Work Calculator
The "Show Work Calculator" is a fundamental tool designed to help users understand the process behind basic mathematical operations. Unlike calculators that simply provide an answer, this tool aims to break down the calculation into clear, sequential steps, making it invaluable for students learning arithmetic and algebra, educators demonstrating concepts, or anyone who wants to reinforce their understanding of how results are derived.
Core Operations and Their Math:
Addition: The process of combining two or more numbers to find their total sum.
Formula:a + b = Sum Example: If you input 10 and 5 and select Addition, the steps would show: 10 + 5 = 15.
Subtraction: The process of taking one number away from another to find the difference.
Formula:a - b = Difference Example: For 10 and 5 with Subtraction: 10 - 5 = 5.
Multiplication: A faster way of adding a number to itself a specified number of times.
Formula:a * b = Product Example: Using 10 and 5 for Multiplication: 10 * 5 = 50.
Division: The process of splitting a number into equal parts or groups.
Formula:a / b = Quotient Example: With 10 and 5 for Division: 10 / 5 = 2. Special attention is paid to avoid division by zero.
Exponentiation (Power): Raising a number (the base) to the power of another number (the exponent) means multiplying the base by itself the number of times indicated by the exponent.
Formula:ab = a * a * ... (b times) Example: If the first number is 3, the exponent is 4: 34 = 3 * 3 * 3 * 3 = 81.
Square Root: Finding the number which, when multiplied by itself, equals the given number. This calculator computes the square root of the *first* number entered.
Formula:sqrt(a) = x such that x * x = a Example: For the first number 16: sqrt(16) = 4, because 4 * 4 = 16.
Percentage: Calculating a specific percentage of a number.
Formula:(Percentage Value / 100) * Number Example: To find 25% of 200: (25 / 100) * 200 = 0.25 * 200 = 50.
Average (Mean): The sum of a set of numbers divided by the count of numbers in the set. For this calculator, it's the average of the two input numbers.
Formula:(a + b) / 2 = Average Example: The average of 10 and 20: (10 + 20) / 2 = 30 / 2 = 15.
Use Cases:
Education: Students can verify their homework answers and understand the methodology.
Teaching: Educators can use it to visually demonstrate calculations to a class.
Self-Learning: Individuals can practice and improve their mathematical skills.
Quick Checks: For simple calculations where showing the steps is beneficial for clarity or auditing.
function updateInputVisibility() {
var operationSelect = document.getElementById("operation");
var selectedOperation = operationSelect.value;
document.getElementById("number2").style.display = ""; // Always show number2 unless it's sqrt
document.getElementById("number2").labels[0].style.display = "";
document.getElementById("exponentDiv").style.display = "none";
document.getElementById("percentageDiv").style.display = "none";
if (selectedOperation === "sqrt") {
document.getElementById("number2").style.display = "none";
document.getElementById("number2").labels[0].style.display = "none";
} else if (selectedOperation === "power") {
document.getElementById("exponentDiv").style.display = "block";
} else if (selectedOperation === "percentage") {
document.getElementById("percentageDiv").style.display = "block";
}
}
function calculate() {
var num1 = parseFloat(document.getElementById("number1").value);
var num2 = parseFloat(document.getElementById("number2").value);
var operation = document.getElementById("operation").value;
var exponent = parseFloat(document.getElementById("exponent").value);
var percentageValue = parseFloat(document.getElementById("percentageValue").value);
var resultDiv = document.getElementById("result");
var stepsDiv = document.getElementById("calculationSteps");
var steps = "";
var finalResult = NaN;
stepsDiv.textContent = ""; // Clear previous steps
resultDiv.textContent = ""; // Clear previous result
// Input validation
if (isNaN(num1)) {
resultDiv.textContent = "Error: Please enter a valid number for 'First Number'.";
return;
}
var validOperation = true;
switch (operation) {
case "add":
if (isNaN(num2)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Second Number' for addition.";
validOperation = false;
} else {
finalResult = num1 + num2;
steps += "Step 1: Add the two numbers.\n";
steps += ` ${num1} + ${num2} = ${finalResult}`;
}
break;
case "subtract":
if (isNaN(num2)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Second Number' for subtraction.";
validOperation = false;
} else {
finalResult = num1 – num2;
steps += "Step 1: Subtract the second number from the first.\n";
steps += ` ${num1} – ${num2} = ${finalResult}`;
}
break;
case "multiply":
if (isNaN(num2)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Second Number' for multiplication.";
validOperation = false;
} else {
finalResult = num1 * num2;
steps += "Step 1: Multiply the two numbers.\n";
steps += ` ${num1} * ${num2} = ${finalResult}`;
}
break;
case "divide":
if (isNaN(num2)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Second Number' for division.";
validOperation = false;
} else if (num2 === 0) {
resultDiv.textContent = "Error: Cannot divide by zero.";
validOperation = false;
} else {
finalResult = num1 / num2;
steps += "Step 1: Divide the first number by the second.\n";
steps += ` ${num1} / ${num2} = ${finalResult}`;
}
break;
case "power":
if (isNaN(exponent)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Exponent'.";
validOperation = false;
} else {
finalResult = Math.pow(num1, exponent);
steps += `Step 1: Raise the base number (${num1}) to the power of the exponent (${exponent}).\n`;
steps += ` ${num1}^${exponent} = ${finalResult}`;
if (exponent === 2) {
steps += "\n(This is called squaring the number.)";
} else if (exponent === 3) {
steps += "\n(This is called cubing the number.)";
}
}
break;
case "sqrt":
finalResult = Math.sqrt(num1);
steps += "Step 1: Calculate the square root of the first number.\n";
steps += ` sqrt(${num1}) = ${finalResult}`;
break;
case "percentage":
if (isNaN(percentageValue)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Percentage Value'.";
validOperation = false;
} else {
finalResult = (percentageValue / 100) * num1;
steps += `Step 1: Convert the percentage value to a decimal by dividing by 100.\n`;
steps += ` ${percentageValue}% = ${percentageValue / 100}\n`;
steps += `Step 2: Multiply the decimal by the base number (${num1}).\n`;
steps += ` ${percentageValue / 100} * ${num1} = ${finalResult}`;
}
break;
case "average":
if (isNaN(num2)) {
resultDiv.textContent = "Error: Please enter a valid number for 'Second Number' to calculate the average.";
validOperation = false;
} else {
finalResult = (num1 + num2) / 2;
steps += "Step 1: Sum the two numbers.\n";
steps += ` ${num1} + ${num2} = ${num1 + num2}\n`;
steps += `Step 2: Divide the sum by 2.\n`;
steps += ` ${num1 + num2} / 2 = ${finalResult}`;
}
break;
default:
resultDiv.textContent = "Error: Invalid operation selected.";
validOperation = false;
}
if (validOperation && !isNaN(finalResult)) {
stepsDiv.textContent = steps;
resultDiv.textContent = "Result: " + finalResult;
} else if (!validOperation) {
// Error message already set in the switch statement
} else {
resultDiv.textContent = "Error: Calculation resulted in an invalid number.";
}
}
// Initialize visibility on page load
window.onload = updateInputVisibility;