Physics
Newton's Second Law
F = m × a
Relates net force to mass and acceleration.
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Chemistry
Ideal Gas Law
PV = nRT
Relates pressure, volume, amount, and temperature of an ideal gas.
Chemistry
Molarity
M = n ÷ V
Expresses solution concentration as moles per liter.
Laboratory
Percent Error
% error = |experimental − accepted| ÷ |accepted| × 100
Compares an experimental result with an accepted reference value.
Physics reference
Physics Formulas
Explore physics formulas for motion, forces, energy, electricity, and mechanics with equations, variables, and calculator tools.
Physics
Newton's Second Law
F = m × a
Relates net force to mass and acceleration.
- Variables
- F = force; m = mass; a = acceleration
Physics
Weight
W = m × g
Calculates the gravitational force acting on a mass.
- Variables
- W = weight; m = mass; g = gravitational acceleration
Physics
Linear Momentum
p = m × v
Finds the momentum of an object in linear motion.
- Variables
- p = momentum; m = mass; v = velocity
Physics
Kinetic Energy
Eₖ = ½mv²
Calculates energy due to an object's motion.
- Variables
- Eₖ = kinetic energy; m = mass; v = velocity
Physics
Mechanical Work
W = Fd cos θ
Calculates work when force acts through a displacement.
- Variables
- W = work; F = force; d = displacement; θ = angle
Physics
Power
P = W ÷ t
Measures how quickly work is done or energy is transferred.
- Variables
- P = power; W = work; t = time
Physics
Density
ρ = m ÷ V
Relates the mass of a substance to its volume.
- Variables
- ρ = density; m = mass; V = volume
Physics
Pressure
P = F ÷ A
Calculates force distributed over a surface area.
- Variables
- P = pressure; F = normal force; A = area
Physics
Ohm's Law
V = I × R
Connects voltage, current, and electrical resistance.
- Variables
- V = voltage; I = current; R = resistance
Physics
Wave Speed
v = f × λ
Relates a wave's speed, frequency, and wavelength.
- Variables
- v = wave speed; f = frequency; λ = wavelength
Physics
Specific Heat
Q = m × c × ΔT
Calculates heat transferred during a temperature change.
- Variables
- Q = heat; m = mass; c = specific heat capacity; ΔT = temperature change
Physics
Velocity Formula
v = d / t
Calculates velocity using displacement divided by time.
- Variables
- v = velocity; d = displacement; t = time
Physics
Average Speed Formula
Average Speed = Total Distance / Total Time
Calculates average speed from total distance and total time.
- Variables
- distance = total distance; time = total time
Physics
Acceleration Formula
a = Δv / t
Calculates acceleration from change in velocity over time.
- Variables
- a = acceleration; Δv = change in velocity; t = time
Physics
Average Velocity Formula
v_avg = Δx / Δt
Calculates average velocity using displacement divided by elapsed time.
- Variables
- v_avg = average velocity; Δx = displacement; Δt = change in time
Physics
Distance Formula
d = v × t
Calculates distance traveled using velocity and time.
- Variables
- d = distance; v = velocity; t = time
Physics
Displacement Formula
Δx = x₂ - x₁
Calculates the change in position between two points.
- Variables
- Δx = displacement; x₂ = final position; x₁ = initial position
Physics
Final Velocity Formula
v = u + at
Calculates final velocity using initial velocity, acceleration, and time.
- Variables
- v = final velocity; u = initial velocity; a = acceleration; t = time
Physics
Time Formula
t = (v - u) / a
Calculates time taken when velocity changes under constant acceleration.
- Variables
- t = time; v = final velocity; u = initial velocity; a = acceleration
Physics
Kinematic Equations Formula
v² = u² + 2as
Relates velocity, acceleration, and displacement for motion with constant acceleration.
- Variables
- v = final velocity; u = initial velocity; a = acceleration; s = displacement
Physics
Projectile Motion Formula
x = v₀t cos(θ), y = v₀t sin(θ) - ½gt²
Describes the horizontal and vertical motion of an object launched at an angle.
- Variables
- v₀ = initial velocity; t = time; θ = launch angle; g = gravitational acceleration
Physics
Free Fall Formula
d = ½gt²
Calculates distance traveled by an object falling under gravity.
- Variables
- d = distance; g = gravitational acceleration; t = time
Physics
Centripetal Acceleration Formula
aᶜ = v² / r
Calculates acceleration toward the center of circular motion.
- Variables
- aᶜ = centripetal acceleration; v = velocity; r = radius
Physics
Centripetal Force Formula
Fᶜ = mv² / r
Calculates the force required to keep an object moving in a circular path.
- Variables
- Fᶜ = centripetal force; m = mass; v = velocity; r = radius
Physics
Angular Velocity Formula
ω = θ / t
Calculates angular velocity from angular displacement over time.
- Variables
- ω = angular velocity; θ = angular displacement; t = time
Physics
Angular Frequency Formula
ω = 2πf
Calculates angular frequency from rotational frequency in circular motion.
- Variables
- ω = angular frequency; f = rotational frequency
Physics
Rotational Frequency Formula
f = ω / 2π
Calculates rotational frequency from angular frequency in circular motion.
- Variables
- f = rotational frequency; ω = angular frequency
Physics
RPM Formula
RPM = 60f
Calculates revolutions per minute from rotational frequency.
- Variables
- RPM = revolutions per minute; f = rotational frequency
Physics
Kinetic Energy Formula
KE = ½mv²
Calculates the energy of an object due to its motion.
- Variables
- KE = kinetic energy; m = mass; v = velocity
Physics
Gravitational Potential Energy Formula
PE = mgh
Calculates stored energy due to an object's height in a gravitational field.
- Variables
- PE = potential energy; m = mass; g = gravitational acceleration; h = height
Physics
Elastic Potential Energy Formula
PE = ½kx²
Calculates energy stored in a stretched or compressed elastic object.
- Variables
- PE = elastic potential energy; k = spring constant; x = displacement
Physics
Work Formula
W = Fd cos(θ)
Calculates work done by a force acting over a displacement.
- Variables
- W = work; F = force; d = displacement; θ = angle between force and motion
Physics
Power Formula
P = W / t
Calculates the rate at which work is completed.
- Variables
- P = power; W = work; t = time
Physics
Mechanical Energy Formula
ME = KE + PE
Calculates total mechanical energy as the sum of kinetic and potential energy.
- Variables
- ME = mechanical energy; KE = kinetic energy; PE = potential energy
Physics
Conservation of Energy Formula
E_total = KE + PE
States that total energy remains constant while energy changes between forms.
- Variables
- E_total = total energy; KE = kinetic energy; PE = potential energy
Physics
Hooke's Law Formula
F = -kx
Calculates the restoring force produced by an elastic spring.
- Variables
- F = spring force; k = spring constant; x = displacement
Physics
Spring Force Formula
F = kx
Calculates the force required to stretch or compress a spring.
- Variables
- F = force; k = spring constant; x = displacement
Physics
Ohm's Law Formula
V = IR
Relates voltage, current, and resistance in an electrical circuit.
- Variables
- V = voltage; I = current; R = resistance
Physics
Electric Power Formula
P = VI
Calculates electrical power using voltage and current.
- Variables
- P = power; V = voltage; I = current
Physics
Coulomb's Law Formula
F = kq₁q₂ / r²
Calculates the electrostatic force between two charged objects.
- Variables
- F = electric force; k = Coulomb constant; q₁ = first charge; q₂ = second charge; r = distance between charges
Physics
Electric Field Formula
E = F / q
Calculates electric field strength from force and charge.
- Variables
- E = electric field; F = electric force; q = charge
Physics
Electric Potential Formula
V = W / q
Calculates electric potential from work done per unit charge.
- Variables
- V = electric potential; W = work done; q = charge
Physics
Voltage Divider Formula
Vout = Vin × R₂ / (R₁ + R₂)
Calculates output voltage across a resistor in a voltage divider circuit.
- Variables
- Vout = output voltage; Vin = input voltage; R₁ = first resistance; R₂ = second resistance
Physics
Current Divider Formula
I₁ = Itotal × R₂ / (R₁ + R₂)
Calculates current distribution between parallel resistors.
- Variables
- I₁ = branch current; Itotal = total current; R₁ = first resistance; R₂ = second resistance
Physics
Capacitance Formula
C = Q / V
Calculates capacitance from stored charge and voltage.
- Variables
- C = capacitance; Q = charge; V = voltage
Physics
Capacitor Energy Formula
E = ½CV²
Calculates the energy stored in a capacitor from capacitance and voltage.
- Variables
- E = stored energy; C = capacitance; V = voltage
Physics
Inductance Formula
L = Φ / I
Relates magnetic flux linkage to current in an inductor.
- Variables
- L = inductance; Φ = magnetic flux linkage; I = current
Physics
Capacitive Reactance Formula
Xc = 1 / (2πfC)
Calculates opposition to alternating current caused by a capacitor.
- Variables
- Xc = capacitive reactance; f = frequency; C = capacitance
Physics
Inductive Reactance Formula
Xl = 2πfL
Calculates opposition to alternating current caused by an inductor.
- Variables
- Xl = inductive reactance; f = frequency; L = inductance
Chemistry reference
Chemistry Formulas
Explore chemistry formulas for reactions, solutions, moles, concentrations, and laboratory calculations with practical tools.
Chemistry
Molarity
M = n ÷ V
Expresses solution concentration as moles per liter.
- Variables
- M = molarity; n = moles of solute; V = solution volume in liters
Chemistry
Molality
m = n ÷ kg solvent
Expresses concentration as moles per kilogram of solvent.
- Variables
- m = molality; n = moles of solute; kg solvent = solvent mass
Chemistry
Solution Dilution
C₁V₁ = C₂V₂
Relates concentration and volume before and after dilution.
- Variables
- C = concentration; V = volume; 1 = initial; 2 = final
Chemistry
Ideal Gas Law
PV = nRT
Relates pressure, volume, amount, and temperature of an ideal gas.
- Variables
- P = pressure; V = volume; n = moles; R = gas constant; T = temperature
Chemistry
pH
pH = −log₁₀[H⁺]
Calculates acidity from the hydrogen ion concentration.
- Variables
- pH = acidity scale value; [H⁺] = hydrogen ion concentration
Chemistry
Percent Yield
% yield = actual ÷ theoretical × 100
Compares the measured product yield with the theoretical yield.
- Variables
- actual = measured yield; theoretical = predicted maximum yield
Chemistry
Mass to Moles
n = m ÷ M
Converts sample mass to amount of substance in moles.
- Variables
- n = moles; m = sample mass; M = molar mass
Chemistry
Mole Fraction
Xᵢ = nᵢ ÷ nₜₒₜₐₗ
Finds a component's fraction of the total amount in a mixture.
- Variables
- Xᵢ = mole fraction; nᵢ = component moles; nₜₒₜₐₗ = total moles
Chemistry
Molarity Formula
M = n / V
Calculates solution concentration using moles of solute divided by solution volume.
- Variables
- M = molarity; n = moles of solute; V = volume of solution
Chemistry
Molality Formula
m = n / kg
Calculates solution concentration using moles of solute per kilogram of solvent.
- Variables
- m = molality; n = moles of solute; kg = kilograms of solvent
Chemistry
Mole Fraction Formula
X = n₁ / n_total
Calculates the ratio of component moles to total moles in a mixture.
- Variables
- X = mole fraction; n₁ = moles of component; n_total = total moles
Chemistry
Dilution Formula
M₁V₁ = M₂V₂
Calculates concentration changes when a solution is diluted.
- Variables
- M₁ = initial concentration; V₁ = initial volume; M₂ = final concentration; V₂ = final volume
Chemistry
Stoichiometry Formula
n = m / M
Relates mass, moles, and molar mass for chemical calculations.
- Variables
- n = number of moles; m = mass; M = molar mass
Chemistry
Molecular Weight Formula
MW = Σ atomic masses
Calculates molecular weight by adding the atomic masses of all atoms in a compound.
- Variables
- MW = molecular weight; atomic masses = masses of atoms
Chemistry
Mass to Moles Formula
n = m / M
Converts between mass and amount of substance using molar mass.
- Variables
- n = moles; m = mass; M = molar mass
Chemistry
Percent Yield Formula
% Yield = (Actual Yield / Theoretical Yield) × 100
Calculates reaction efficiency by comparing actual and theoretical product amounts.
- Variables
- Actual Yield = measured product; Theoretical Yield = expected product
Chemistry
pH Formula
pH = -log[H⁺]
Calculates the acidity of a solution using hydrogen ion concentration.
- Variables
- pH = acidity measure; [H⁺] = hydrogen ion concentration
Chemistry
pOH Formula
pOH = -log[OH⁻]
Calculates the basicity of a solution using hydroxide ion concentration.
- Variables
- pOH = basicity measure; [OH⁻] = hydroxide ion concentration
Chemistry
Ideal Gas Law Formula
PV = nRT
Relates pressure, volume, temperature, and amount of gas.
- Variables
- P = pressure; V = volume; n = moles; R = gas constant; T = temperature
Chemistry
Gas Density Formula
ρ = PM / RT
Calculates gas density using pressure, molar mass, temperature, and the gas constant.
- Variables
- ρ = gas density; P = pressure; M = molar mass; R = gas constant; T = temperature
Laboratory reference
Laboratory Formulas
Explore laboratory formulas for measurements, uncertainty, statistics, and experimental data analysis.
Laboratory
Percent Error
% error = |experimental − accepted| ÷ |accepted| × 100
Compares an experimental result with an accepted reference value.
- Variables
- experimental = measured value; accepted = reference value
Laboratory
Percent Difference
% difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
Compares two experimental values when neither is an accepted value.
- Variables
- A = first value; B = second value
Laboratory
Arithmetic Mean
x̄ = Σx ÷ n
Calculates the average of a set of observations.
- Variables
- x̄ = mean; Σx = sum of values; n = number of values
Laboratory
Sample Standard Deviation
s = √(Σ(xᵢ − x̄)² ÷ (n − 1))
Measures the spread of sample observations around their mean.
- Variables
- s = sample standard deviation; xᵢ = each value; x̄ = sample mean; n = sample size
Laboratory
Coefficient of Variation
CV = s ÷ x̄ × 100
Expresses variability relative to the mean as a percentage.
- Variables
- CV = coefficient of variation; s = standard deviation; x̄ = mean
Laboratory
Relative Uncertainty
relative uncertainty = absolute uncertainty ÷ |measured value|
Shows measurement uncertainty relative to the measured magnitude.
- Variables
- absolute uncertainty = uncertainty in original units; measured value = reported result
Laboratory
Average Rate of Change
rate = (y₂ − y₁) ÷ (x₂ − x₁)
Calculates the average change in one variable per unit change in another.
- Variables
- y = dependent variable; x = independent variable
Laboratory
Linear Regression
y = mx + b
Models a straight-line relationship between two variables.
- Variables
- m = slope; b = y-intercept; x = input; y = predicted output
Laboratory
Mean Formula
x̄ = Σx / n
Calculates the average value of a set of experimental measurements.
- Variables
- x̄ = mean; Σx = sum of values; n = number of values
Laboratory
Median Formula
Middle value of ordered data
Finds the central value of a sorted dataset.
- Variables
- ordered data = sorted values
Laboratory
Standard Deviation Formula
σ = √(Σ(x - μ)² / N)
Measures the spread and variability of experimental data.
- Variables
- σ = standard deviation; x = individual value; μ = mean; N = number of values
Laboratory
Percent Error Formula
% Error = |Experimental - Accepted| / Accepted × 100
Measures the difference between an experimental value and an accepted value.
- Variables
- Experimental = measured value; Accepted = reference value
Laboratory
Percent Difference Formula
% Difference = |A - B| / ((A + B) / 2) × 100
Compares two experimental values without a reference value.
- Variables
- A = first value; B = second value
Laboratory
Measurement Uncertainty Formula
U = ± value
Represents the range of possible variation in a scientific measurement.
- Variables
- U = uncertainty; measured value = experimental measurement
Laboratory
Coefficient of Variation Formula
CV = (σ / μ) × 100
Measures relative variability of data compared with its mean.
- Variables
- CV = coefficient of variation; σ = standard deviation; μ = mean
Laboratory
Significant Figures Rules
Precision depends on reported digits
Determines the correct number of significant figures in scientific measurements and calculations.
- Variables
- significant digits = meaningful measurement digits
Formula help
Frequently Asked Questions
How should I use a science formula?
Identify the known values, convert them to compatible units, substitute them into the equation, and keep extra digits until the final rounding step.
Can I rearrange these formulas to solve for another variable?
Yes. Apply the same inverse operation to both sides of the equation until the unknown variable is isolated, then check that the resulting units make sense.
Why can a calculator result differ from my manual answer?
Differences usually come from unit conversion, rounding too early, sign conventions, or using a formula outside its assumptions.
Do these formulas replace experimental judgment?
No. A formula is a model. Always consider measurement uncertainty, significant figures, experimental conditions, and the assumptions behind the equation.