Formula: Average = (Sum of all numbers) / (Total count)
This formula is used to calculate the mean or average value of a set of numbers.
Formula: SI = (P × R × T) / 100
This formula calculates the simple interest earned on a principal amount (P) at a certain rate (R) over time (T).
Formula: CI = P(1 + R/100)^T - P
This formula calculates compound interest, where interest is calculated on both the principal amount and the accumulated interest.
Formula: Speed = Distance / Time
Used to calculate the speed of an object by dividing the total distance traveled by the time taken.
Formula: Profit % = (Profit / Cost Price) × 100
This formula calculates the profit percentage based on the cost price and profit earned.
Formula: Loss % = (Loss / Cost Price) × 100
Calculates the percentage loss relative to the cost price.
Formula: h² = p² + b²
This formula is used to calculate the hypotenuse (h) of a right-angled triangle when the lengths of the perpendicular (p) and base (b) are known.
Formula: x = (-b ± √(b² - 4ac)) / 2a
This formula gives the solutions for the roots of a quadratic equation ax² + bx + c = 0.
Formula: Area = πr²
The area of a circle is calculated by squaring the radius (r) and multiplying it by π (approximately 3.14159).
Formula: Circumference = 2πr
This formula calculates the circumference (the perimeter) of a circle.
Formula: Area = l × b
The area of a rectangle is calculated by multiplying the length (l) and breadth (b).
Formula: Perimeter = 2(l + b)
The perimeter of a rectangle is the sum of all its sides, calculated by adding the length (l) and breadth (b), then multiplying by 2.
Formula: Area = (1/2) × b × h
The area of a triangle is calculated by multiplying the base (b) by the height (h) and dividing by 2.
Formula: Work = Force × Distance
Work done is the product of the force applied and the distance moved in the direction of the force.
Formula: Force = Mass × Acceleration
Force is calculated by multiplying the mass of an object by its acceleration, as per Newton's Second Law of Motion.
Formula: Pressure = Force / Area
This formula calculates pressure by dividing force by the area over which the force is applied.
Formula: Power = Work / Time
Power is the rate at which work is done, calculated by dividing the work by the time taken to perform it.
Formula: Density = Mass / Volume
Density is the mass of an object per unit volume.
Formula: Momentum = Mass × Velocity
Momentum is the product of the mass and velocity of an object.
Formula: F = G(m1 × m2) / r²
This is the gravitational force formula between two masses (m1 and m2) separated by a distance r, where G is the gravitational constant.
Formula: F = m × a
Newton's second law of motion, where F is the force, m is the mass, and a is the acceleration.
Formula: V = I × R
Ohm's Law relates the voltage (V), current (I), and resistance (R) in an electrical circuit.
Formula: Power = Voltage × Current
Electric power is the product of voltage and current in a circuit.
Formula: Energy = Power × Time
Electric energy is the product of power and the time for which it is consumed.
Formula: Acceleration = (Final Velocity - Initial Velocity) / Time
Acceleration is the change in velocity over time.
Formula: Vout = Vin × (R2 / (R1 + R2))
This formula is used to calculate the output voltage in a resistor voltage divider circuit.
Formula: Q = mcΔT
This formula calculates the heat energy (Q) required to change the temperature of a substance, where m is mass, c is specific heat capacity, and ΔT is the change in temperature.
Formula: ΔS = Q/T
Entropy is a measure of disorder in a system. This formula relates change in entropy (ΔS) to heat (Q) and temperature (T).
Formula: c = Q / (m × ΔT)
Specific heat is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius.
Formula: KE = ½ mv²
Kinetic energy is the energy possessed by an object due to its motion, calculated by multiplying half of its mass by the square of its velocity.
Formula: PE = mgh
Potential energy is the energy an object possesses due to its position, calculated as the product of mass (m), gravitational acceleration (g), and height (h).
Formula: v = fλ
The speed of a wave is the product of its frequency (f) and wavelength (λ).
Formula: f = 1/T
Frequency is the inverse of the period (T), representing the number of cycles per unit time.
Formula: λ = v/f
Wavelength is the distance between two consecutive points of the same phase in a wave, calculated by dividing wave speed (v) by frequency (f).
Formula: Rs = R1 + R2 + R3 + ...
The total resistance in a series circuit is the sum of individual resistances.
Formula: 1/Rp = 1/R1 + 1/R2 + 1/R3 + ...
The total resistance in a parallel circuit is found by taking the reciprocal of the sum of the reciprocals of the individual resistances.
Formula: 1/Cs = 1/C1 + 1/C2 + ...
The total capacitance in a series circuit is found by taking the reciprocal of the sum of the reciprocals of individual capacitances.
Formula: Cp = C1 + C2 + C3 + ...
The total capacitance in a parallel circuit is the sum of individual capacitances.
Formula: F = q(E + v × B)
The Lorentz force is the force experienced by a charged particle moving in an electromagnetic field, where q is charge, E is the electric field, and B is the magnetic field.
Formula: P = ρgh
Fluid pressure is the pressure exerted by a fluid in a column, where ρ is the fluid density, g is gravitational acceleration, and h is the height of the fluid column.
Formula: P1V1 = P2V2
Boyle's law describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature.
Formula: V1/T1 = V2/T2
Charles' law states that the volume of a gas is directly proportional to its temperature when pressure is constant.
Formula: V/n = k
Avogadro's law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.
Formula: P + ½ρv² + ρgh = constant
Bernoulli's principle states that the total mechanical energy of a flowing fluid remains constant under ideal conditions.
Formula: n1 sin θ1 = n2 sin θ2
Snell's law describes the relationship between the angles of incidence and refraction when light passes between two media with different refractive indices.
Formula: 1/f = 1/u - 1/v
This formula relates the focal length (f), object distance (u), and image distance (v) in a lens.
Formula: 1/f = 1/v + 1/u
The mirror formula relates the focal length (f), object distance (u), and image distance (v) for a spherical mirror.
Formula: E = mc² / sqrt(1 - v²/c²)
This formula is derived from Einstein's theory of relativity, relating energy, mass, and velocity for objects moving at relativistic speeds.
Formula: E = mc²
Einstein's famous equation that shows the equivalence of mass and energy, where E is energy, m is mass, and c is the speed of light.
Formula: r = n²h² / (4π²me²)
This formula calculates the radius of the orbit of an electron in a hydrogen atom according to the Bohr model.