All Formulas Hub
Welcome to your central resource for essential formulas across Mathematics, Physics, and Chemistry. Here you'll find detailed explanations, practical examples, and quick-access links to our comprehensive formula collections.
All Formulas -
Welcome to your central resource for essential formulas. Jump directly to the subject you need—each section below provides a glimpse into our detailed formula collections.
Mathematics Formulas
Algebra, geometry, trigonometry, and calculus. Essential equations for every student.
Physics Formulas
From mechanics to modern physics. Unlock the principles that govern the universe.
Chemistry Formulas
Chemical reactions, stoichiometry, and the periodic table explained.
Conversion Formulas
Quickly convert units for temperature, length, mass, and more.
Mathematics Formulas
Mathematics is the language of the universe. From simple arithmetic to complex calculus, formulas are the tools that help us describe relationships, solve problems, and understand patterns. Below is a selection of fundamental formulas from various branches of mathematics.
Quadratic Formula
x = [-b ± √(b² - 4ac)] / 2a
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.
Pythagorean Theorem
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.
Area of a Circle
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.
Slope of a Line
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.
Physics Formulas
Physics seeks to understand the fundamental principles of the universe, from the smallest subatomic particles to the largest galaxies. Formulas in physics are concise expressions of these principles, allowing us to predict the behavior of physical systems.
Newton's Second Law of Motion
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.
Kinetic Energy
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.
Ohm's Law
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.
Chemistry Formulas
Chemistry is the study of matter and the changes it undergoes. Chemical formulas and equations are symbolic representations of molecules, compounds, and their interactions during chemical reactions, forming the basis of our understanding of the material world.
Ideal Gas Law
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.
Molar Mass Calculation
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.
Density Formula
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.
Conversion Formulas
Unit conversion is a fundamental skill in science and daily life. These formulas allow you to switch between different measurement systems, such as metric and imperial, ensuring consistency and accuracy in your calculations.
Temperature Conversion (Celsius to Fahrenheit)
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.
Length Conversion (Meters to Feet)
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.
Mass Conversion (Kilograms to Pounds)
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.
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