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Searchable scientific equation repository. Tweak variables inline, review step-by-step derivations, study worked examples, and take quick concept checks.
States that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Calculates the attractive force of gravity between two masses separated by a center-to-center distance r.
Relates potential difference (Voltage), electrical current, and electrical resistance in an ideal conductor.
The energy that an object possesses due to its motion.
Specifies the concentration of a chemical solute in a solution as moles of solute per liter of total solution volume.
The equation of state of a hypothetical ideal gas. It relates pressure, volume, gas quantity, and absolute temperature.
Measures the acidity or basicity of an aqueous solution by calculating the negative logarithm of hydrogen ion concentration.
Relates concentration and volume before and after diluting a stock solution, maintaining conservation of solute moles.
Momentum is the product of an object's mass and velocity. It is a vector quantity conserved in isolated systems.
States that the restoring force exerted by a spring is proportional to its extension or compression from natural length.
Relates the speed of a wave to its frequency and wavelength. Applies to all transverse and longitudinal waves.
Relates the focal length of a thin lens to the object distance and image distance. Used in optics for camera lenses, eyeglasses, and microscopes.
Pressure is the force applied per unit area. It is a scalar quantity fundamental to fluid mechanics and atmospheric science.
Power is the rate of doing work or transferring energy. It measures how quickly energy is used.
Energy stored in an object due to its position in a gravitational field. Increases with height and mass.
Describes the electrostatic force between two point charges. Attractive for opposite charges, repulsive for like charges.
Describes how light bends when it passes from one medium into another with a different refractive index.
The net inward force required to keep an object moving in a circular path at constant speed.
The rate at which electrical energy is consumed or produced in a circuit.
The horizontal range of a projectile launched at angle θ with initial speed v₀ on level ground.
The percentage of input energy that is converted to useful output energy. Losses are due to heat, friction, and sound.
The time for one complete oscillation of a pendulum depends only on its length and local gravity, not on amplitude or mass.
Describes how a solid material expands linearly when heated. α is a material-specific coefficient.
Work is done when a force causes displacement. Only the component of force parallel to displacement contributes.
In a series circuit, resistances add directly. The same current flows through all resistors.
In a parallel circuit, the reciprocals of resistances add. Total resistance is always less than the smallest individual resistance.
Molar mass is the mass of one mole of a substance, equal to the sum of atomic masses of all atoms in its formula.
Gives the percentage by mass that each element contributes to a compound's molar mass.
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature.
Predicts spontaneity of a reaction. A negative ΔG means the reaction is spontaneous under the given conditions.
Used to calculate the pH of a buffer solution from the pKa of the weak acid and the ratio of conjugate base to acid concentrations.
Kc expresses the ratio of product concentrations to reactant concentrations at equilibrium, each raised to their stoichiometric coefficients.
The mass of substance deposited at an electrode is proportional to the charge passed and the molar mass, inversely proportional to the number of electrons transferred.
The pressure required to prevent osmosis across a semipermeable membrane. Proportional to solute molarity and absolute temperature.
The overall equation for photosynthesis. Plants convert carbon dioxide and water into glucose and oxygen using light energy absorbed by chlorophyll.
Glucose is broken down using oxygen to release energy in the form of ATP. The process occurs in the cytoplasm and mitochondria.
Describes allele and genotype frequencies in a non-evolving population. p = dominant allele frequency, q = recessive allele frequency.
A measure of the proportion of cells undergoing mitosis in a tissue sample. Used in cancer diagnosis and cell biology experiments.
The volume of blood pumped by the heart per minute. Equal to stroke volume times heart rate.
The rate of diffusion across a membrane is proportional to surface area and concentration gradient, and inversely proportional to membrane thickness.
Models population growth when resources are unlimited. N₀ is initial population, r is intrinsic growth rate, t is time.
Water potential (ψ) determines the direction of water movement by osmosis. Water moves from high to low water potential.
Net Primary Productivity is the energy available to consumers after plants use some for their own respiration (R) from total photosynthesis (GPP).
The proportion of a specific allele among all allele copies in a population for a particular gene.
The percentage of energy transferred from one trophic level to the next. Typically about 10%, meaning 90% is lost as heat and metabolic processes.
Tests whether observed genetic ratios match expected Mendelian ratios. A high χ² value suggests the deviation from expectation is not due to chance alone.
Describes the rate of an enzyme-catalysed reaction as a function of substrate concentration. Vmax is maximum rate; Km is the substrate concentration at half-Vmax.
Relates the absorbance of light by a solution to the concentration of the solute. Widely used in colorimetric assays and protein quantification.