All Formulas Hub

Definition: This formula provides the roots or solutions of a quadratic equation. The term inside the square root, (b² - 4ac), is called the discriminant, which determines the nature of the roots (real, complex, or repeated).
Example: Solve x² + 5x + 6 = 0. Here, a=1, b=5, c=6.
x = [-5 ± √(5² - 4*1*6)] / (2*1)
x = [-5 ± √(25 - 24)] / 2
x = [-5 ± √1] / 2
So, x = (-5 + 1) / 2 = -2 and x = (-5 - 1) / 2 = -3.

Definition: The square of the hypotenuse (the side opposite the right angle, c) is equal to the sum of the squares of the other two sides (a and b).
Example: If a side `a` = 8 and the hypotenuse `c` = 10, find the other side `b`.
8² + b² = 10²
64 + b² = 100
b² = 100 - 64 = 36
b = √36 = 6.

Definition: This formula calculates the area (A) of a circle based on its radius (r), which is the distance from the center to any point on the edge. π (pi) is a constant approximately equal to 3.14159.

Definition: The slope (m) of a line measures its steepness and is calculated as the change in the vertical coordinate (rise) divided by the change in the horizontal coordinate (run) between any two distinct points on the line.

Definition: The force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). This is a cornerstone of classical mechanics.
Example: If a 10 kg object accelerates at 2 m/s², the force is F = 10 kg * 2 m/s² = 20 Newtons.

Definition: Kinetic energy (KE) is the energy an object possesses due to its motion. It is determined by the mass (m) of the object and the square of its velocity (v).
Example: A 2 kg ball moving at 3 m/s has KE = 0.5 * 2 * (3)² = 9 Joules.

Definition: A fundamental principle in electricity, Ohm's law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, where R is the constant of proportionality, known as resistance.

Definition: This equation describes the state of a hypothetical ideal gas. It relates the pressure (P), volume (V), number of moles (n), and temperature (T) of the gas. R is the ideal gas constant.

Definition: Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance (moles). It connects the macroscopic property of mass to the microscopic property of moles.

Definition: Density (ρ) is a measure of mass (m) per unit of volume (V). It's a fundamental property of matter that describes how tightly packed its constituent particles are.

Definition: Converts a temperature from the Celsius scale to the Fahrenheit scale. This is commonly used when comparing weather reports or scientific data from different regions.
Example: Convert 20°C to Fahrenheit.
°F = (20 × 9/5) + 32 = 36 + 32 = 68°F.

Definition: Converts a length from meters (metric system) to feet (imperial system). One meter is approximately equal to 3.281 feet.
Example: Convert a 100-meter dash to feet.
feet ≈ 100 × 3.281 = 328.1 feet.

Definition: Converts mass from kilograms (metric system) to pounds (imperial system). This is useful for measurements in fitness, cooking, and shipping.
Example: Convert a mass of 70 kg to pounds.
pounds ≈ 70 × 2.205 = 154.35 pounds.