Newton's Second Law
F = m × a
Relates net force to mass and acceleration.
- Variables
- F = force; m = mass; a = acceleration
Quick-reference equations
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Physics reference
Physics Formulas
Weight
W = m × g
Calculates the gravitational force acting on a mass.
- Variables
- W = weight; m = mass; g = gravitational acceleration
Linear Momentum
p = m × v
Finds the momentum of an object in linear motion.
- Variables
- p = momentum; m = mass; v = velocity
Kinetic Energy
Eₖ = ½mv²
Calculates energy due to an object's motion.
- Variables
- Eₖ = kinetic energy; m = mass; v = velocity
Mechanical Work
W = Fd cos θ
Calculates work when force acts through a displacement.
- Variables
- W = work; F = force; d = displacement; θ = angle
Power
P = W ÷ t
Measures how quickly work is done or energy is transferred.
- Variables
- P = power; W = work; t = time
Density
ρ = m ÷ V
Relates the mass of a substance to its volume.
- Variables
- ρ = density; m = mass; V = volume
Pressure
P = F ÷ A
Calculates force distributed over a surface area.
- Variables
- P = pressure; F = normal force; A = area
Ohm's Law
V = I × R
Connects voltage, current, and electrical resistance.
- Variables
- V = voltage; I = current; R = resistance
Wave Speed
v = f × λ
Relates a wave's speed, frequency, and wavelength.
- Variables
- v = wave speed; f = frequency; λ = wavelength
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
Chemistry reference
Chemistry Formulas
Molarity
M = n ÷ V
Expresses solution concentration as moles per liter.
- Variables
- M = molarity; n = moles of solute; V = solution volume in liters
Molality
m = n ÷ kg solvent
Expresses concentration as moles per kilogram of solvent.
- Variables
- m = molality; n = moles of solute; kg solvent = solvent mass
Solution Dilution
C₁V₁ = C₂V₂
Relates concentration and volume before and after dilution.
- Variables
- C = concentration; V = volume; 1 = initial; 2 = final
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
pH
pH = −log₁₀[H⁺]
Calculates acidity from the hydrogen ion concentration.
- Variables
- pH = acidity scale value; [H⁺] = hydrogen ion concentration
Percent Yield
% yield = actual ÷ theoretical × 100
Compares the measured product yield with the theoretical yield.
- Variables
- actual = measured yield; theoretical = predicted maximum yield
Mass to Moles
n = m ÷ M
Converts sample mass to amount of substance in moles.
- Variables
- n = moles; m = sample mass; M = molar mass
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
Laboratory reference
Laboratory Formulas
Percent Error
% error = |experimental − accepted| ÷ |accepted| × 100
Compares an experimental result with an accepted reference value.
- Variables
- experimental = measured value; accepted = reference value
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
Arithmetic Mean
x̄ = Σx ÷ n
Calculates the average of a set of observations.
- Variables
- x̄ = mean; Σx = sum of values; n = number of values
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
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
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
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
Linear Regression
y = mx + b
Models a straight-line relationship between two variables.
- Variables
- m = slope; b = y-intercept; x = input; y = predicted output
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.