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Finance, maths, physics, and everyday formulas — pick one, fill in the fields, and keep what you use in favourites and history.
100 formulas
Finance
J = C · i · t
Interest calculated only on the original principal.
Finance
M = C · (1 + i)^t
Interest that accumulates on principal plus previously earned interest.
Finance
a → b ; c → x ⇒ x = (b · c) / a
If a corresponds to b, what corresponds to c? Use for directly proportional quantities.
Finance
a → b ; c → x ⇒ x = (a · b) / c
For inversely proportional quantities: more of one means less of the other.
Finance
P = V · p / 100
How much is p% of a given value.
Finance
Δ% = (Vf − Vi) / Vi · 100
How much a value grew or shrank, in percent.
Finance
p = a / b · 100
Expresses one value as a percentage of another.
Finance
Vf = V · (1 − d / 100)
Final price after applying a percentage discount.
Finance
Vf = V · (1 + t / 100)
Final price after adding a percentage on top.
Finance
FV = P · ((1 + i)^n − 1) / i
How much a recurring deposit becomes after n periods.
Finance
PV = FV / (1 + i)^n
What a future amount is worth today at a given rate.
Finance
PMT = PV · i / (1 − (1 + i)^−n)
Fixed payment that pays off a loan over n periods.
Finance
ROI = (G − C) / C · 100
Percentage gain relative to what was invested.
Finance
M = (P − C) / P · 100
Margin is profit over price; markup is profit over cost.
Finance
Q = CF / (P − CV)
How many units must be sold to cover fixed costs.
Finance
G = C · p / 100
Tip amount, total with tip, and share per person.
Mathematics
A = a²
Side multiplied by itself.
Mathematics
A = b · h
Base times height — the everyday area of rooms, walls, and land.
Mathematics
A = (b · h) / 2
Half of base times height.
Mathematics
A = π · r²
Pi times the radius squared.
Mathematics
A = ((B + b) / 2) · h
Average of the two parallel sides times the height.
Mathematics
A = (D · d) / 2
Product of the diagonals divided by two.
Mathematics
A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) / 2
Useful for land plots where you can only measure the sides.
Mathematics
C = 2 · π · r
Distance around a circle.
Mathematics
P = 2 · (b + h)
Total length around a rectangle — fences, frames, baseboards.
Mathematics
A = (θ / 360) · π · r²
A slice of a circle defined by its central angle.
Mathematics
V = a³
Side raised to the third power.
Mathematics
V = c · l · h
Length times width times height — boxes, tanks, rooms.
Mathematics
V = π · r² · h
Base circle area times height — water tanks, cans, pipes.
Mathematics
V = (4/3) · π · r³
Four thirds of pi times the radius cubed.
Mathematics
V = (1/3) · π · r² · h
One third of the equivalent cylinder.
Mathematics
A = 4 · π · r²
Four times pi times the radius squared.
Mathematics
A = 2 · π · r · (r + h)
Both circular ends plus the side wall — useful for painting or wrapping.
Mathematics
c = √(a² + b²)
The diagonal of a right triangle from its two legs.
Mathematics
b = √(c² − a²)
One leg from the hypotenuse and the other leg.
Mathematics
d = √((x₂ − x₁)² + (y₂ − y₁)²)
Straight-line distance on a plane.
Mathematics
m = (y₂ − y₁) / (x₂ − x₁)
Rate of change between two points, also given as a percentage grade.
Mathematics
x = (−b ± √Δ) / 2a, Δ = b² − 4ac
Roots of ax² + bx + c = 0. A negative discriminant means no real roots.
Mathematics
M = Σ(n · p) / Σp
Average of three values with weights. Leave the weights at 1 for a simple average.
Mathematics
n! = n · (n − 1) · … · 1
Product of all whole numbers from 1 to n.
Mathematics
A(n,k) = n! / (n − k)!
How many ordered sequences of k items you can draw from n.
Mathematics
C(n,k) = n! / (k! · (n − k)!)
How many groups of k items you can pick from n — lottery odds, committees.
Mathematics
aₙ = a₁ + (n − 1) · d
Any term of a sequence that grows by a constant amount.
Mathematics
Sₙ = n · (a₁ + aₙ) / 2
Sum of the first n terms.
Physics
v = Δs / Δt
Distance covered divided by the time it took.
Physics
s = s₀ + v · t
Position after travelling at constant speed.
Physics
a = (v − v₀) / Δt
How fast the speed itself changes.
Physics
v = v₀ + a · t
Speed after accelerating for a given time.
Physics
s = s₀ + v₀ · t + a · t² / 2
Position under constant acceleration — braking distance, free fall.
Physics
v = √(v₀² + 2 · a · Δs)
Final speed from a distance, with no need to know the time.
Physics
F = m · a
Force equals mass times acceleration.
Physics
P = m · g
The pull of gravity on a mass.
Physics
Ec = m · v² / 2
Energy stored in movement — grows with the square of the speed.
Physics
Ep = m · g · h
Energy stored by height above a reference point.
Physics
Ee = k · x² / 2
Energy stored in a stretched or compressed spring.
Physics
W = F · d · cos θ
Force times displacement, accounting for the angle between them.
Physics
P = W / Δt
How much work is done per unit of time.
Physics
Q = m · v
Mass times velocity — what is conserved in collisions.
Physics
I = F · Δt
Force applied over a period of time.
Physics
d = m / V
Mass per unit of volume.
Physics
p = F / A
Force spread over an area.
Physics
p = ρ · g · h
Pressure at a given depth in a liquid.
Physics
E = ρ · V · g
Upward force on a submerged volume (Archimedes).
Physics
U = R · I
Voltage equals resistance times current.
Physics
P = U · I
Voltage times current, with the resulting current draw and resistance.
Physics
kWh = P · h · d / 1000
Turn an appliance’s wattage and daily use into monthly kWh and money.
Physics
R = R₁ + R₂ + R₃
Series resistances simply add up.
Physics
1/R = 1/R₁ + 1/R₂ + 1/R₃
Leave R₃ empty or at zero to use only two resistors.
Physics
f = 1 / T
Frequency is the inverse of the period.
Physics
v = λ · f
Wavelength times frequency.
Physics
Q = m · c · ΔT
Energy needed to heat or cool a mass. Water’s specific heat is 4186 J/kg·°C.
Physics
P = n · R · T / V (R = 8,314)
Pressure of n moles of gas at a temperature in kelvin.
Physics
a꜀ = v² / r
Acceleration toward the centre of a curve.
Physics
F = G · m₁ · m₂ / d²
Attraction between two masses (G = 6,674·10⁻¹¹).
Health & everyday
IMC = m / h²
Weight relative to height. Between 18.5 and 24.9 is the usual healthy range.
Health & everyday
TMB = 88,36 + 13,4·m + 4,8·h − 5,68·idade
Calories burned at rest (Harris-Benedict).
Health & everyday
TMB = 447,59 + 9,25·m + 3,10·h − 4,33·idade
Calories burned at rest (Harris-Benedict).
Health & everyday
m = IMC · h²
The weight interval that keeps BMI between 18.5 and 24.9.
Health & everyday
V = m · 35
Around 35 ml of water per kilogram of body weight.
Health & everyday
RCA = cintura / altura
Below 0.5 is generally considered low risk.
Health & everyday
FCmáx = 220 − idade
Rough estimate used to plan training intensity.
Health & everyday
FC = (220 − idade) · p / 100
The beats per minute for a chosen percentage of your maximum.
Health & everyday
pace = tempo / distância
Minutes per kilometre and the equivalent speed.
Health & everyday
kcal = MET · 3,5 · m / 200 · min
Uses the activity MET: walking ≈ 3.5, cycling ≈ 8, running ≈ 10.
Health & everyday
consumo = km / litros
How far the car goes per litre, and litres per 100 km.
Health & everyday
custo = (km / consumo) · preço
How much fuel a trip needs and what it costs.
Health & everyday
preço unitário = preço / quantidade
Compare packages of different sizes at the supermarket.
Health & everyday
litros = área · demãos / rendimento
Litres of paint from the area, number of coats, and coverage per litre.
Health & everyday
peças = área / área da peça · (1 + perda/100)
Number of pieces including a waste allowance for cuts.
Health & everyday
nova = qtd · (porções desejadas / porções originais)
Adjust an ingredient quantity for a different number of servings.
Conversions
°F = °C · 9/5 + 32 | °C = (°F − 32) · 5/9
Enter one number and read it interpreted both ways.
Conversions
K = °C + 273,15 | °C = K − 273,15
Absolute temperature differs from Celsius by 273.15.
Conversions
mi = km / 1,609344 | km = mi · 1,609344
One mile is 1.609344 kilometres.
Conversions
lb = kg / 0,45359237 | kg = lb · 0,45359237
One pound is 0.45359237 kilograms.
Conversions
ft = m / 0,3048 | m = ft · 0,3048
One foot is exactly 0.3048 metres.
Conversions
in = cm / 2,54 | cm = in · 2,54
One inch is exactly 2.54 centimetres.
Conversions
m/s = km/h / 3,6 | km/h = m/s · 3,6
Divide by 3.6 to go from km/h to m/s.
Conversions
gal = L / 3,785411784 | L = gal · 3,785411784
One US gallon is 3.785411784 litres.
Conversions
ft² = m² · 10,7639 | m² = ft² / 10,7639
One square metre is about 10.7639 square feet.
Conversions
rad = ° · π / 180 | ° = rad · 180 / π
Half a turn is 180 degrees or π radians.