This calculator allows you to compute results based on various mathematical and scientific formulas. Select a formula from the dropdown to adjust the input fields accordingly.
Area of Rectangle (A = l * w)
Area of Circle (A = π * r²)
Pythagorean Theorem (c = √(a² + b²))
Quadratic Formula (x = [-b ± √(b² – 4ac)] / 2a)
Distance Formula (d = √[(x₂ – x₁)² + (y₂ – y₁)²])
Simple Interest (I = P * r * t)
Result will appear here
Understanding Mathematical Formulas and Their Applications
Mathematical formulas are concise expressions that represent relationships between quantities. They are the backbone of science, engineering, economics, and many other fields, providing a universal language to describe and predict phenomena. This calculator is designed to handle a few common and fundamental formulas, illustrating the power of mathematical abstraction and computation.
Featured Formulas:
1. Area of a Rectangle: A = l * w
This is one of the most basic geometric formulas. It calculates the space enclosed within a rectangle. 'l' represents the length and 'w' represents the width of the rectangle. The unit of the area will be the square of the unit used for length and width (e.g., if length and width are in meters, the area is in square meters).
Example:
If length (l) = 10 units and width (w) = 5 units,
Area = 10 * 5 = 50 square units.
2. Area of a Circle: A = π * r²
This formula calculates the area enclosed within a circle. 'π' (pi) is a mathematical constant approximately equal to 3.14159. 'r' represents the radius of the circle (the distance from the center to any point on the edge). The result is in square units.
Example:
If radius (r) = 7 units, and π ≈ 3.14159,
Area = 3.14159 * (7²) = 3.14159 * 49 ≈ 153.938 square units.
Fundamental to geometry, this theorem applies to right-angled triangles. It states that the square of the hypotenuse ('c', the side opposite the right angle) is equal to the sum of the squares of the other two sides ('a' and 'b', the legs). This formula is crucial in trigonometry, navigation, and construction.
Example:
If side a = 3 units and side b = 4 units,
c² = 3² + 4² = 9 + 16 = 25
c = √25 = 5 units.
4. Quadratic Formula: x = [-b ± √(b² – 4ac)] / 2a
This powerful formula solves quadratic equations of the form ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients and 'a' is not zero. It provides the values of 'x' (the roots) that satisfy the equation. The term inside the square root (b² – 4ac) is called the discriminant, which determines the nature of the roots (real or complex).
Derived from the Pythagorean theorem, this formula calculates the straight-line distance between two points (x₁, y₁) and (x₂, y₂) in a Cartesian coordinate system. It's widely used in geometry, physics, and mapping.
Example:
Distance between (2, 3) and (5, 7):
d = √[(5 – 2)² + (7 – 3)²]
d = √[3² + 4²] = √[9 + 16] = √25 = 5 units.
6. Simple Interest: I = P * r * t
Simple interest is a method of calculating the interest charge on a loan. 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (expressed as a decimal), and 't' is the time the money is invested or borrowed for, in years. It's a straightforward way to calculate interest, unlike compound interest.
Example:
Principal (P) = $1000, Rate (r) = 5% per year (0.05), Time (t) = 2 years.
Interest (I) = 1000 * 0.05 * 2 = $100.
By providing a platform to compute these formulas, we aim to aid students, educators, and professionals in quickly verifying calculations and understanding the practical application of mathematical principles.
function updateInputs() {
var formulaSelect = document.getElementById("formulaSelect");
var selectedFormula = formulaSelect.value;
var inputArea = document.getElementById("inputArea");
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = "Result will appear here"; // Reset result on formula change
inputArea.innerHTML = ""; // Clear previous inputs
if (selectedFormula === "area_rectangle") {
inputArea.innerHTML = `
`;
}
}
function calculate() {
var formulaSelect = document.getElementById("formulaSelect");
var selectedFormula = formulaSelect.value;
var resultDiv = document.getElementById("result");
var result = "";
if (selectedFormula === "area_rectangle") {
var length = parseFloat(document.getElementById("length").value);
var width = parseFloat(document.getElementById("width").value);
if (isNaN(length) || isNaN(width) || length <= 0 || width <= 0) {
result = "Please enter valid positive numbers for length and width.";
} else {
var area = length * width;
result = "Area = " + area.toFixed(2);
}
} else if (selectedFormula === "area_circle") {
var radius = parseFloat(document.getElementById("radius").value);
var pi = Math.PI;
if (isNaN(radius) || radius <= 0) {
result = "Please enter a valid positive number for the radius.";
} else {
var area = pi * Math.pow(radius, 2);
result = "Area = " + area.toFixed(2);
}
} else if (selectedFormula === "pythagorean_theorem") {
var side_a = parseFloat(document.getElementById("side_a").value);
var side_b = parseFloat(document.getElementById("side_b").value);
if (isNaN(side_a) || isNaN(side_b) || side_a <= 0 || side_b <= 0) {
result = "Please enter valid positive numbers for sides a and b.";
} else {
var hypotenuse_squared = Math.pow(side_a, 2) + Math.pow(side_b, 2);
var hypotenuse = Math.sqrt(hypotenuse_squared);
result = "Hypotenuse (c) = " + hypotenuse.toFixed(2);
}
} else if (selectedFormula === "quadratic_formula") {
var a = parseFloat(document.getElementById("coeff_a").value);
var b = parseFloat(document.getElementById("coeff_b").value);
var c = parseFloat(document.getElementById("coeff_c").value);
if (isNaN(a) || isNaN(b) || isNaN(c)) {
result = "Please enter valid numbers for coefficients a, b, and c.";
} else if (a === 0) {
result = "Coefficient 'a' cannot be zero for a quadratic equation.";
} else {
var discriminant = b * b – 4 * a * c;
if (discriminant < 0) {
// Handle complex roots if needed, for simplicity here we'll state there are no real roots
result = "No real roots (discriminant is negative).";
} else {
var x1 = (-b + Math.sqrt(discriminant)) / (2 * a);
var x2 = (-b – Math.sqrt(discriminant)) / (2 * a);
result = "x₁ = " + x1.toFixed(4) + ", x₂ = " + x2.toFixed(4);
}
}
} else if (selectedFormula === "distance_formula") {
var x1 = parseFloat(document.getElementById("x1").value);
var y1 = parseFloat(document.getElementById("y1").value);
var x2 = parseFloat(document.getElementById("x2").value);
var y2 = parseFloat(document.getElementById("y2").value);
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) {
result = "Please enter valid numbers for all coordinates.";
} else {
var deltaXSquared = Math.pow(x2 – x1, 2);
var deltaYSquared = Math.pow(y2 – y1, 2);
var distance = Math.sqrt(deltaXSquared + deltaYSquared);
result = "Distance (d) = " + distance.toFixed(4);
}
} else if (selectedFormula === "simple_interest") {
var principal = parseFloat(document.getElementById("principal").value);
var ratePercent = parseFloat(document.getElementById("rate").value);
var time = parseFloat(document.getElementById("time").value);
if (isNaN(principal) || isNaN(ratePercent) || isNaN(time)) {
result = "Please enter valid numbers for principal, rate, and time.";
} else if (principal <= 0 || ratePercent < 0 || time <= 0) {
result = "Principal and time must be positive. Rate cannot be negative.";
}
else {
var rateDecimal = ratePercent / 100;
var interest = principal * rateDecimal * time;
var totalAmount = principal + interest;
result = "Interest (I) = " + interest.toFixed(2) + "; Total Amount = " + totalAmount.toFixed(2);
}
}
resultDiv.innerHTML = result;
}
// Initialize with the first formula's inputs
document.addEventListener('DOMContentLoaded', updateInputs);