Formulas you can check by hand
Sometimes the equation matters as much as the answer. These pages show the formula, define the variables, walk through sample numbers, and point back to the calculator when you are done checking the work.
Start with the equation when you need to check the work by hand. Open the calculator when you just need the number.
Formulas by topic
Pick a formula to see the variables, sample numbers, and the mistakes that usually throw the answer off.
Loan payment
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
See the loan payment formula, each variable, examples, and a link to the Loan Calculator.
Mortgage payment
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
See the mortgage payment formula, each variable, examples, and a link to the Mortgage Calculator.
Break-even point
Break-even units = fixed costs / (price per unit - variable cost per unit)
See the break-even point formula, each variable, examples, and a link to the Break-Even Analysis Calculator.
Cap rate
Cap rate = NOI / property value * 100
See the cap rate formula, each variable, examples, and a link to the Cap Rate Calculator.
Compound interest
A = P(1 + r / n)^(n * t)
See the compound interest formula, each variable, examples, and a link to the Compound Interest Calculator.
Inflation-adjusted value
FV = PV * (1 + i)^t
See the inflation-adjusted value formula, each variable, examples, and a link to the Inflation Calculator.
Marketing ROI
Marketing ROI = (revenue - marketing cost) / marketing cost * 100
See the marketing roi formula, each variable, examples, and a link to the Marketing ROI Calculator.
Monthly savings needed
PMT = (FV - PV(1 + r)^n) / (((1 + r)^n - 1) / r)
See the monthly savings needed formula, each variable, examples, and a link to the Savings Goal Calculator.
Net operating income
NOI = gross operating income - operating expenses
See the net operating income formula, each variable, examples, and a link to the NOI Calculator.
Net present value
NPV = -C0 + sum(Ct / (1 + r)^t)
See the net present value formula, each variable, examples, and a link to the NPV Calculator.
Price per square foot
Price per square foot = price / area
See the price per square foot formula, each variable, examples, and a link to the Price Per Square Foot Calculator.
Profit margin
Profit margin = profit / revenue * 100
See the profit margin formula, each variable, examples, and a link to the Profit Margin Calculator.
Return on investment
ROI = (gain - cost) / cost * 100
See the return on investment formula, each variable, examples, and a link to the Investment ROI Calculator.
Calorie deficit
daily intake = TDEE - daily deficit
See the calorie deficit formula, each variable, examples, and a link to the Calorie Deficit Calculator.
BMI
BMI = weight_kg / height_m^2
See the bmi formula, each variable, examples, and a link to the BMI Calculator.
BMR
BMR = 10W + 6.25H - 5A + S
See the bmr formula, each variable, examples, and a link to the BMR Calculator.
Navy body fat
male: BF% = 495 / (1.0324 - 0.19077log10(waist - neck) + 0.15456log10(height)) - 450
See the navy body fat formula, each variable, examples, and a link to the Body Fat Calculator.
Maximum heart rate
max heart rate = 220 - age
See the maximum heart rate formula, each variable, examples, and a link to the Heart Rate Calculator.
Brzycki one-rep max
1RM = weight * 36 / (37 - reps)
See the brzycki one-rep max formula, each variable, examples, and a link to the One Rep Max Calculator.
Karvonen heart rate
target HR = resting HR + (max HR - resting HR) * intensity
See the karvonen heart rate formula, each variable, examples, and a link to the Heart Rate Calculator.
TDEE
TDEE = BMR * activity multiplier
See the tdee formula, each variable, examples, and a link to the TDEE Calculator.
Waist-to-height ratio
WHtR = waist circumference / height
See the waist-to-height ratio formula, each variable, examples, and a link to the Waist-to-Height Ratio Calculator.
Weeks to weight goal
weeks = weight to lose / weekly loss rate
See the weeks to weight goal formula, each variable, examples, and a link to the Calorie Deficit Calculator.
Factorial
n! = n * (n - 1) * ... * 2 * 1
See the factorial formula, each variable, examples, and a link to the Factorial Calculator.
Percentage of a number
result = percent / 100 * number
See the percentage of a number formula, each variable, examples, and a link to the Percentage Calculator.
Combination
C(n, r) = n! / (r! * (n - r)!)
See the combination formula, each variable, examples, and a link to the Probability Calculator.
Percentage change
percentage change = (new value - original value) / abs(original value) * 100
See the percentage change formula, each variable, examples, and a link to the Percentage Change Calculator.
Probability
P(event) = favorable outcomes / total outcomes
See the probability formula, each variable, examples, and a link to the Probability Calculator.
Slope
m = (y2 - y1) / (x2 - x1)
See the slope formula, each variable, examples, and a link to the Slope Calculator.
Mean
mean = sum of values / number of values
See the mean formula, each variable, examples, and a link to the Mean Median Mode Calculator.
Median
median = middle sorted value, or average of the two middle sorted values
See the median formula, each variable, examples, and a link to the Mean Median Mode Calculator.
What percent
percent = part / whole * 100
See the what percent formula, each variable, examples, and a link to the Percentage Calculator.
Ratio simplification
a:b simplified = (a / gcd(a, b)):(b / gcd(a, b))
See the ratio simplification formula, each variable, examples, and a link to the Ratio Calculator.
Proportion
a / b = c / d
See the proportion formula, each variable, examples, and a link to the Ratio Calculator.
Acceleration
a = (v - v0) / t
See the acceleration formula, each variable, examples, and a link to the Acceleration Calculator.
Density
rho = m / V
See the density formula, each variable, examples, and a link to the Density Calculator.
Electrical power
P = V * I
See the electrical power formula, each variable, examples, and a link to the Electrical Power Calculator.
Force
F = m * a
See the force formula, each variable, examples, and a link to the Force Calculator.
Gravitational potential energy
PE = m * g * h
See the gravitational potential energy formula, each variable, examples, and a link to the Potential Energy Calculator.
Kinetic energy
KE = 0.5 * m * v^2
See the kinetic energy formula, each variable, examples, and a link to the Kinetic Energy Calculator.
Momentum
p = m * v
See the momentum formula, each variable, examples, and a link to the Momentum Calculator.
Ohm's law
V = I * R
See the ohm's law formula, each variable, examples, and a link to the Ohm's Law Calculator.
Power
P = W / t
See the power formula, each variable, examples, and a link to the Work and Power Calculator.
Pressure
P = F / A
See the pressure formula, each variable, examples, and a link to the Pressure Calculator.
Velocity
v = d / t
See the velocity formula, each variable, examples, and a link to the Velocity Calculator.
Wave speed
v = f * lambda
See the wave speed formula, each variable, examples, and a link to the Wave Calculator.
Work
W = F * d
See the work formula, each variable, examples, and a link to the Work and Power Calculator.
Just need the answer?
The calculator directory is the shortest path from inputs to a result.