MCAT Equations
Name
Equation
Units
Mechanics & Energy
∆x
∆t
∆d
∆t
∆v
∆t
Average speed
Average velocity
Acceleration
Newton’s Second Law
F!"# = ma
Static Friction
F!,!"# = µ! F!
Kinetic Friction
F! = µ! F!
Force of gravity acting
perpendicular to an
inclined plane
Force of gravity acting
parallel to an inclined
plane
m
s
m
s
m
s!
m
1 Newton = 1 kg ∙ !
s
m
1 Newton = 1 kg ∙ !
s
m
1 Newton = 1 kg ∙ !
s
mgcosθ
m
1 Newton = 1 kg ∙ !
s
mgsinθ
m
1 Newton = 1 kg ∙ !
s
Torque
τ = rFsinθ
N∙m
Work
W = Fdcosθ
1 Joule = N ∙ m
Work (pressurevolume curve)
W = P∆V
J
Center of mass
Mechanical Advantage
Power
Power
x=
m! x! + m! x! + m! x!
m! + m! + m!
F!"#
MA =
F!"
W ∆E
P=
=
t
t
P = Fv
1 watt W =
W
J
s
Kinetic Energy
1
KE = mv !
2
J
Work-Kinetic Energy
theorem
W!"# = ∆KE = K ! − K !
J
Gravitational Potential
Energy
U = mgh
J
Elastic Potential
Energy
1
U = kx !
2
J
Hooke’s Law
F = −kx
N
Frequency of a wave
f=
Speed of a wave
v = fλ
1
T
1
= Hz
s
m
s
Fluids
m
V
Density
ρ=
Specific Gravity
ρ!"#$%&
ρ!"#$%
Buoyant Force
F! = mg = ρ!"#$% Vg
Pascal’s Law
F! F!
=
A! A!
Hydrostatic Pressure
P = P! + ρgz
Poiseuille’s Law
πr ! ∆P
Q=
8ηL
Continuity Equation
A! v! = A! v!
Bernoulli’s Equation
1
P! + ρv!! + ρgh! = P! …
2
Gases
Absolute Temperature
K = ℃ + 273
Pressure
P=
F
A
g
cm!
N
Ideal Gas Law
PV = nRT
Boyle’s Law
P! V! = P! V!
V! V!
=
T! T!
n! n!
=
V! V!
Charles’ Law
Avogadro’s Law
Average kinetic
energy of a gas
particle
Heat capacity at
constant volume for
an ideal monatomic
gas
Heat capacity at
constant pressure for
an ideal monatomic
gas
van der Waals
equation of state
Dalton’s Law of Partial
Pressures
3
KE!"# = k ! T
2
J
3
C! = nR
2
J
K
5
C! = nR
2
J
K
P=
nRT
n! a
− !
V − nb V
P! = X! P!
P = P! + P! + P!
Thermodynamics
Heat transferred
q = mc∆T
Standard Heat of
Reaction
°
∆H!,!"#$%&'(
−
°
∆H!,!"#$%#&%'
Standard Heat of
Reaction
°
∆H!"#$%
!"#$%& −
°
∆H!"#$%
!"#$%&
Change in Gibbs Free
Energy
Linear Expansion
(Solids)
Volumetric
Expansions (Solids &
Liquids)
∆G = ∆H − T∆S
∆L = αL∆T
∆V = βV∆T
1
cal
J
= 4.184
g∙K
g∙K
kJ
mol
Sound
I
I!
Sound Level
β = 10log
Sound Level
β! = β! + 10log
Intensity
Doppler Effect
dB
I!
I!
P
A
v ± v!
f! = f
v ∓ v!
I=
λ=
Waves in Open Pipes
f=
f=
W
m!
Hz
2L
n
v nv
=
λ 2L
λ=
Waves in Closed Pipes
dB
4L
n
v nv
=
λ 4L
Light & Electromagnetic Radiation
Speed of Light
c = fλ
Energy of Photon
E = hf
m
s
Geometrical Optics
Law of Reflection
𝜃! = 𝜃!
Index of Refraction
n=
Snell’s Law
n! sinθ! = n! sinθ!
Critical Angle
𝜃! = 𝑠𝑖𝑛!!
c
v
n!
n!
Focal length of lenses
in a series
1 1 1 2
= + =
f o i
r
−i
m=
o
1
P=
f
1 1 1 1
1
= + + + ⋯+
f f! f! f!
f!
Power of lenses in a
series
P = P! + P! + P! + ⋯ + P!
Magnification for a
system of lenses
m = m! × m! × m!
Optics Equation
Magnification
Lens Power
diopters
diopters
Electrostatics
Voltage (Potential
Difference)
kq! q!
r!
F! kQ!
E=
= !
q
r
kQq
U=
r
U kQ
V= =
q
r
V
d
W!"
∆V = V! − V! =
q
Power
VI
W
Power
V!
R
W
Power
I! R
W
Coulomb’s Law
Electric Field
Electrical Potential
Energy
Electrical Potential
Intensity of Uniform
Electric Field
F! =
N
N
V
or
C
m
J
1V=1
J
C
V
m
Volts
Circuits
Q
t
Current
I=
Ohm’s Law
V = IR
1A=1
C
s
Resistors in Series
Resistors in Parallel
Resistivity
Capacitance
Energy of a Charged
Capacitor
Capacitors in Series
Capacitors in Parallel
R ! = R! + R ! + R !
1
1
1
1
=
+
+
𝑅! 𝑅! 𝑅! 𝑅!
𝑅∙𝐴
𝜚=
𝐿
𝑄
𝐴
𝐶 = = 𝜀!
𝑉
𝑑
!
Q
1
1
U=
= Q∆V = C(∆V)!
C
2
2
1
1
1
1
= + +
𝐶! 𝐶! 𝐶! 𝐶!
𝐶! = 𝐶! + 𝐶! + 𝐶!
Ohms (Ω)
Ω
Ohm-meter (Ω ∙ m)
1F=1
C
V
F
F
Magnetism
Magnetic Force
F! = qvBsinθ
Lorentz Force
F = qE + qvBsinθ
1T=1
N∙s
m∙C
Atomic Structure & Stoichiometry
Maximum number of
electrons in a shell
2n!
Kinetic Energy of a
Photoelectron
hf − ϕ
eV
Bonding & Reactions
Formal Charge
1
FC = V − NB − B
2
Dipole Moment
p=q∙d
C∙m
Specific rotation
α =
α!"#
c×l
degrees
Electrochemistry
Electrodeposition
Equation
mol M =
It
nF
Cell potential
cell pot. = red. pot − ox. pot
Kinetics
Rate law
rate = k A ! B !
Arrhenius Equation
k = Ae !"
Law of Mass Action
C!D!
k !" =
A!B!
!!!
Molecular Structure & Absorbance Spectra
Wavenumber
1
λ
cm!!
Solutions
Autoionization of
water
K ! = H! O! OH ! = 10!!"
pH
− log H !
pOH
− log OH !
Acid Dissociation
Constant
Base Dissociation
Constant
H! O! A!
k! =
HA
!
B OH !
k! =
BOH
pK !
−logK !
pK !
−logK !
HendersonHasselbalch
Point of Inflection
Solubility Product
Constant
pH = pK ! + log
[Conj. base]
[acid]
pH = pK ! or 14 − pK !
for A! B! :
K !" = A!! ! B !! !
Separations & Purifications
Retardation factor
R! =
distance spot moved
distance solvent front moved
Circulation & Respiration
Henry’s Law
A = K ! × P!
Amino Acids & Proteins
Electrophoresis
(migration velocity of
a molecule)
v=
Ez
f
Genetics
p+q=1
Hardy-Weinberg
p! + 2pq + q! = 1
Enzymes
Michaelis-Menten
v=
v!"# S
K ! + [S]
Plasma Membrane & Nervous System
Nernst Equation
Osmotic Pressure
°
E!"## = E!"##
−
RT
ln (Q)
nF
Π = iMRT
0