Browse All Math Formulas by Category
Mathematics is the universal language that powers science, technology, and everyday life. Whether you're a student, teacher, engineer, or simply a math enthusiast, having quick access to essential math formulas is crucial. Explore our organised categories below to find exactly what you need — each topic links directly to its full formula page with definitions, proofs, worked examples, and an interactive calculator.
At Danielitte, each formula comes with a thorough explanation of how it was derived, making it far more effective than rote memorisation. With over 329 formula pages covering Geometry, Algebra, Trigonometry, Calculus, Analytical Geometry, Matrices, Statistics, Transforms, and more — this is your complete free reference.
Geometry
Master the formulas that measure and define the world's shapes.
- Triangle
- Right Triangle
- Square
- Rectangle
- Parallelogram
- Lozenge
- Trapezoid
- Convex Quadrilateral
- Circle
- Segment of Circle
- Sector of Circle
- Regular Poligon of N Sides
- Hexagon
- Sphere
- Sperical Cap
- Sperical Segment
- Sperical Sector
- Torus
- Cylinder
- Cone
- Frustum of Right Circular Cone
- Pyramid
- Cuboid
- Triangular Prism
Trignometry
Master the relationships between angles and sides in triangles and beyond.
- Trigonometric Functions For A Right Triangle
- Trigonometric Table
- Co-Ratios
- Basic Formulas
- Multiple Angle Formulas
- Powers Of Trigonometric Functions
- Formulas With T=tan(x/2)
- Addition Formulas
- Sum Of Trigonometric Functions
- Product Of Trigonometric Functions
- Half Angle Formulas
- Angles Of A Plane Triangle
- Sides And Angles Of A Plane Triangle
- Relationships Among Trigonometric Fuctions
Equations
Master the art of problem-solving with essential equation formulas.
- Linear Equation
- System of Two Linear Equation
- Quadratic Equation
- Exponential Equation
- Logarithmic Equation
- Trigonometric Equation Cos
- Trigonometric Equation Sin
- Trigonometric Equation Tan
- Trigonometric Equation Cotan
- Linear Inequation
- Quadratic Inequation
- Exponential Inequation
- Logarithmic Inequation
- Trigonometric Inequation Cos
- Trigonometric Inequation Sin
- Trigonometric Inequation Tan
- Trigonometric Inequation Cotan
- Constant
- Absolute
- Square Root
- Parabolic
- Cubic
- Reciprocal
- Sec
- Cosec
- Horizontal Shifting
- Vertical Shifting
- Reflection
- streching
Analytical Geometry
Bridging geometry and algebra with coordinates, equations, and graphs.
- Points
- A Triangle
- Equation of Line
- Equation of Circle
- Ellipse
- Hyperbola
- Parabola
- Line
- Equation of Line Joining Two Points A,B
- Plane
- Equation of Sphere Center at M and Radius R in Rectangular Coordinates
- Equation of Ellipsoid With Center M and Semi-Axes A,B,C
- Elliptic Cylinder With Axis as Z Axis
- Elliptic Cone With Axis as Z Axis
- Hyperboloid of One Sheets
- Hyperboloid of Two Sheets
- Elliptic Paraboloid
- Hyperbolic Paraboloid
Statistics
Master the formulas that turn raw data into meaningful insights.
- Set
- Subset
- Intersection
- Union
- Relative Complement of A in B
- Absolute Complement
- Symmetric Difference
- Operations On Sets
- Combinations
- Permutations
- Probability
- Mean
- Median
- Mode
- Example
- Geometric Mean
- Harmonic Mean
- Variance
- Standard Deviation
- Root Mean Square
- Normal Distribution(gaussion Distribution)
- Exponential Distribution
- Poisson Distribution
- Uniforn Distribution
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Over 329 formulas across all major mathematical disciplines
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Whether you're preparing for an exam, solving real-world problems, or just brushing up on your skills, our formula collection is designed to make learning math intuitive and efficient.
📖 Bookmark This PageFrequently Asked Questions about Math Formulas
Perimeter is the one-dimensional distance around the boundary of a shape, like a fence around a yard. Area is the two-dimensional space inside the shape, like the amount of grass inside the fence.
Pi (π) is a special mathematical constant representing the fixed ratio of a circle's circumference to its diameter. Because this ratio is the same for all circles, Pi is a fundamental part of calculating their circumference and area.
The concept of a variable is arguably the most important, as it allows us to represent unknown quantities and describe general relationships. Mastering how to manipulate and solve for variables is the core skill of algebra.
Different logarithm bases are useful in different contexts. The decimal logarithm (base 10) is common in science due to our number system, while the natural logarithm (base e) describes continuous growth and is fundamental in calculus.
Trigonometry is primarily used to study the relationships between the angles and side lengths of triangles. This allows us to find unknown dimensions and angles in geometric figures and has wide-ranging applications in fields like physics, engineering, and astronomy.
Sine, cosine, and tangent are the three main trigonometric functions, defined as ratios of sides in a right triangle. Sine is the ratio of the opposite side to the hypotenuse, cosine is the adjacent side to the hypotenuse, and tangent is the opposite side to the adjacent side.
An equation states that two expressions are exactly equal, using an '=' sign. An inequation, or inequality, compares two expressions, stating that one is greater than, less than, or not equal to the other, often resulting in a range of solutions.
The ± symbol indicates that a quadratic equation can have up to two distinct real solutions. One solution is found by adding the square root term, and the other is found by subtracting it.
Analytical geometry, also known as coordinate geometry, is a branch of mathematics that studies geometry using a coordinate system. It uses algebra to define and analyze geometric shapes like lines, circles, and planes as equations.
A circle is a set of points equidistant from a single center point. An ellipse is a set of points where the sum of the distances from two fixed points (foci) is constant, which gives it its oval shape.
A derivative is the instantaneous rate of change of a function. Think of it as the exact speed of a car at a specific moment, not its average speed over a trip.
The derivative is the output or the result, which is a new function that tells you the slope of the original. Differentiation is the actual process or method you use to find that derivative.
An indefinite integral finds the general antiderivative of a function, which is a family of functions resulting in an expression with a '+ C'. A definite integral calculates a single numerical value, representing the area under the curve between two specific points.
The derivative of any constant is zero, so when we find an antiderivative, there is an unknown constant that would have disappeared during differentiation. The '+ C' represents this entire family of possible constants, making the antiderivative general.
Matrix addition is performed element-wise and requires matrices to have the same dimensions. Matrix multiplication follows a more complex row-by-column rule and has different dimensional requirements.
No, matrix multiplication is generally not commutative. This means that for two matrices A and B, the product A times B is usually not equal to B times A.
The key difference is order. In permutations, the order of the items matters (like a passcode), while in combinations, the order does not matter (like picking a team of players).
Set theory provides the formal language for probability. The set of all possible outcomes is the 'sample space', and 'events' are subsets of that sample space, allowing us to precisely define what we are measuring.
A Fourier Series represents a periodic function as a sum of discrete sine and cosine waves. A Fourier Transform is a generalization for non-periodic functions, representing them as a continuous spectrum of frequencies.
The frequency domain reveals the underlying periodic components of a signal that are often hidden in the time domain. This makes it easier to design filters, identify noise, and understand system responses.
Distance is a scalar quantity that measures the total path covered. Displacement is a vector quantity that represents the shortest straight-line path from the starting point to the ending point, including direction.
Air resistance is a complex force that depends on an object's speed, shape, and size. Ignoring it allows us to focus on the fundamental principles of gravity and motion, providing a good approximation for many scenarios.
Electric force is the push or pull between two specific charges, as described by Coulomb's Law. An electric field is a property of space created by a source charge, representing the force that *would* be exerted per unit of a positive test charge placed at any point.
A capacitor stores energy in the electric field created between its two conductive plates when they hold opposite charges. Work is done to separate these charges, and this work is stored as electric potential energy in the field.
Gas laws like Charles's Law show that volume is directly proportional to temperature. This relationship only holds true on an absolute scale like Kelvin, where 0 K represents absolute zero and there are no negative values.
An ideal gas is a theoretical model where gas particles have no volume and do not interact with each other. Real gases deviate from this model, especially at high pressures and low temperatures, but the Ideal Gas Law is a very good approximation under many conditions.
Periodic motion is any motion that repeats itself in a regular time interval. Simple Harmonic Motion (SHM) is a specific type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium.
The standard formula for the period of a simple pendulum is derived using the approximation that sin(θ) ≈ θ for small angles. This simplifies the complex differential equation of motion into one that describes SHM, making it much easier to solve.
Reflection occurs when light bounces off a surface, like a mirror, with the angle of incidence equaling the angle of reflection. Refraction is the bending of light as it passes from one medium to another, like light entering water, which is described by Snell's Law.
The refractive index of a material is a dimensionless number that describes how fast light travels through it. A higher refractive index means light travels slower and bends more when entering the material from air.
Atomic physics studies the atom as a whole, focusing on the arrangement and behavior of its electrons in energy shells. Nuclear physics zooms in on the nucleus itself, studying protons, neutrons, and the powerful forces that bind them.
Einstein's E=mc^2 shows that mass is a highly concentrated form of energy. In nuclear reactions, a small amount of mass can be converted into a vast amount of energy, and vice versa.
Physical constants are crucial because they represent fundamental, unchanging properties of the universe. They ensure that scientific equations are consistent and can be used to make accurate predictions about physical phenomena.
A constant has a fixed, unchanging value, like the elementary charge. A variable is a quantity that can change or take on different values within a problem, such as velocity or position.