# Must-Know Science Formulas for the HiSET Test

Achieving proficiency in science can be challenging. If you’re studying for the HiSET Science Test, you’re probably facing that challenge. This test covers a number of scientific disciplines and includes concepts in chemistry, biology, and physics. And formulas can be instrumental in all of them. In addition to knowing the formulas and how to use them, you’ll need to understand when to use them and how they relate to relevant topics. So much to remember! That’s why practice and experience using formulas are needed.

We have created the following charts with the essential formulas you’ll need for all the science areas and the topics within them. Our charts combine theory and math so you can remember complex concepts with a single and short equation. Think of them as your own personal toolbox!

You can practice using these equations using our free sample questions.

## Formulas for the Chemistry and Biology Questions

Formula Symbols Comment
$$S_u \cdot \frac{D_u}{S_u} = D_u$$ $$S_u$$ = starting unit
$$D_u$$ = desired unit
$$\frac{D_u}{S_u}$$ = conversion factor
Multiple steps may
be necessary.
$$a \cdot b\% = a \cdot \frac{b}{100}$$ a = any real number
b% = any percent
Remember to simplify
if possible.
% change = $$\frac{b-a}{a} \cdot 100\%$$ a = original value
b = new value
The percent may be
positive or negative.
$$d = \frac{m}{v}$$ d = density (g/$$cm^3$$)
m = mass (g)
v = volume ($$cm^3$$)

$$^A_ZX$$ A = Mass number
Z = atomic number (number of protons)
X = atom symbol

A = Z + N A = mass number
Z = atomic number (number of protons)
N = number of neutrons

$$a = n \cdot N_a$$ a = number of atoms
n = number of moles
$$N_a$$ = Avogadro’s number ($$6.022 \times 10^23$$)

$$MM = \frac{m}{n}$$ MM = molar mass (g\mole)
m = mass (g)
n = number of moles

$$m_r = m_p$$ $$m_r$$ = mass of reactants (g)
$$m_p$$ = mass of reactants (g)
Conservation of mass
$$k = Ae^{\frac{-E_a}{RT}}$$ k = rate constant
A = frequency factor
$$E_a$$ = activation energy (kJ/mol)
R = ideal gas constant ($$0.0821 \frac{L \cdot atm}{mol \cdot K}$$)
Arrhenius equation
$$P \cdot V = n \cdot R \cdot T$$ P = pressure (atm)
V = volume (L)
n = number of moles
R = ideal gas constant ($$0.0812\frac{L \cdot atm}{mol \cdot K}$$)
T = temperature (K)
Ideal gas equation
$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$ $$P_1 ,V_1, T_1$$ = original pressure, volume, and temperature
$$P_2, V_2, T_2$$ = final pressure, volume, and temperature
$$T_1, T_2$$ units are K.
Combined gas law
$$pH = - log[H_3O^+]$$ pH = measure of solution acidity
$$[H_3O^+]$$ = hydronium ion concentration (mol/L)

$$14 = pH + pOH$$ pH = measure of solution acidity
pOH = measure of solution basicity

$$K$$ = $$^\circ C + 273$$

$$^\circ C = \frac{5}{9} \cdot (^\circ F - 32)$$
$$K$$ = temperature in Kelvin
$$^\circ C$$ = temperature in degrees Celsius
$$^\circ F$$ = temperature in degrees Fahrenheit
Temperature
Conversion
$$\overline x = \frac{\Sigma x_i}{n}$$ $$\overline x$$ = mean
$$x_i$$ = value of each measurement
n = number of measurements

Median = $$\left(\frac{n+1}{2}\right)^{th}$$ term n = number of measurements (if odd)
Median =$$\frac{\left(\frac{n}{2}\right)^{th} term + \left(\frac{n}{2}+1 \right)^{th} term}{2}$$ n = number of measurements (if even)
$$s = \sqrt{\frac { \Sigma (x_i - \overline{x})^2 } {n-1})}$$ s = standard deviation
$$\overline{x}$$ = mean
$$x_i$$ = value of each measurement
n = number of measurements

$$V=s^2$$ V = variance
s = standard deviation

$$CV = RSD = 100 \cdot \frac{s}{\overline{x}}$$ CV = coefficient of variation
RSD = relative standard deviation
s = standard deviation
$$\overline{x}$$ = mean

$$r=\frac{dx}{dt}$$ r = rate of change
dx = amount of change
dt = change in time

$$\frac{dN}{dt} = B-D$$ dN = change in population size
dt = change in time
B = birth rate
D = death rate
Population growth
$$\frac{dN}{dt} = r_{max} \cdot N$$ dN = change in population size
dt = change in time
$$r_{max}$$ = maximum growth rate of population
N = population size
Exponential growth
$$\frac{dN}{dt} = r_{max} \cdot N \cdot \left(\frac{K-N}{K}\right)$$ dN = change in population size
dt = change in time
$$r_{max}$$ = maximum growth rate of population
N = population size
K = carrying capacity
Logistic growth

## Formulas for the Position, Motion, and Mechanical Energy Questions

Formula Symbols Comment
$$d=vt$$
$$v_f =v_o + at$$
$$\Delta d = \left(\frac{v_f+v_o}{2}\right)\Delta t$$
$$d = d_o + v_ot + \frac{1}{2} at^2$$
$$v_f^2 = v_o^2 + 2ad$$
$$d$$ = displacement(m)
$$d_o$$ = initial position (m)
$$t$$ = time (s)
$$v$$ = velocity (m/s)
$$v_o$$= initial velocity (m/s)
$$v_f$$= final velocity (m/s)
$$a$$ = acceleration (m/s$$^2$$)
Kinematics
$$F=m \cdot a$$ F = force (N)
m = mass (kg)
a = acceleration (m/s$$^2$$)

$$I = F \cdot t$$ I = impulse (N $$\cdot$$ s)
F = force (N)
t = time (s)

$$F=\frac{G \cdot m_1 \cdot m_2}{d^2}$$ F = force (N)
G = $$6.67 \times 10^{-11} N \cdot m^2 kg^-2$$
$$m_n$$ = mass n (kg)
d = distance (m)
Newton’s Law
of Gravitation
$$F = \frac{\Delta p}{\Delta t}$$
$$p = m \cdot v$$
F = force (N)
p = momentum (kg $$\cdot$$m/s}
m = mass (kg)
v = velocity(m/s)
Momentum
$$KE = \frac{1}{2}m \cdot v^2$$
$$GPE = m \cdot g \cdot h$$
$$EPE = \frac{1}{2} k \cdot x^2$$
$$E_t = KE + PE$$
KE = kinetic energy (J)
m = mass (kg)
v = velocity (m/s)
GPE = gravitational potential energy (J)
g = acceleration of gravity (m/s$$^2$$)
h = height (m)
EPE = elastic potential energy (J)
k = spring constant (N/m)
x = spring displacement (m)
E$$_t$$ = total mechanical energy (J)
Energy
$$W= \Delta E = F \cdot d \cdot cos\theta$$
$$P= \frac {W}{t}$$
W = work (N $$\cdot$$ m)
E$$_t$$= total mechanical energy (J)
F = force (N)
d = displacement (m)
$$\theta$$ = angle between force and displacement
P = power (W)
t = time (s)

## Formulas for the Wave, Electricity, and Magnetism Questions

Formula Symbols Comment
$$\nu=f\lambda$$ $$\nu$$ = speed (m/s)
f = frequency (Hz)
$$\lambda$$ = wavelength (m)

$$n = \frac{c}{v}$$ n = index of refraction
c = speed of light in a vacuum (m/s)
v = speed of light in the medium (m/s)

$$n_1sin\theta_1 = n_2 sin \theta_2$$ $$n_1$$ = index of refraction in medium 1
$$n_2$$ = index of refraction in medium 2
$$\theta_1$$ = angle of incidence
$$\theta_2$$ = angle of refraction
Snell’s Law
$$\frac{1}{f} = \frac{1}{d_i} + \frac{1}{d_o}$$ f = focal length (m)
$$d_i$$ = image distance (m)
$$d_o$$ = object distance (m)

$$M= \frac{h_i}{h_o} = \frac{d_i}{d_o}$$ M = magnification
$$h_i$$ = image height (m)
$$h_o$$ = object height (m)
$$d_i$$ image distance (m)
$$d_o$$ = object distance (m)

$$E = n \cdot h \cdot f$$ E = energy (J)
n = number of particles
h = Planck constant ($$J \cdot s$$)
f = frequency (Hz)

$$F = \frac{K \cdot q_1 \cdot q_2}{r^2}$$ F = force (N)
K = Coulomb constant ($$9 \times 10^9 N \cdot m^2/C^2)$$
$$q_n$$ = charge on each particle (C)
r = center to center distance between particles (m)

$$E=\frac{F}{q}$$ E = electric field (N/C)
F = force (N)
C charge (C)

$$C = \frac{q}{V}$$ C = capacitance (F)
q = charge (C)
V = electric potential or potential difference (V)

$$I = \frac{q}{t}$$ I = current (A)
q = charge (C)
t = time (s)

$$V = \frac{E}{q} = \frac{W}{q}$$ V = electric potential or potential difference
E = energy (J)
W = work (J)
q = charge (C)

$$R = \frac{\rho I}{A} = \frac{V}{I} = \frac{P}{I}$$ R = resistance ($$\Omega$$)
$$\rho$$ = resistivity ($$\Omega \cdot m$$)
l = length (m)
A = cross-sectional area ($$m^2$$)
V = electric potential or potential difference (V)
P = power (W)
I = current (A)

$$P = I^2R = VI = \frac{V^2}{R}$$ P = power (W)
I current (A)
R = resistance ($$\Omega$$)
V = electric potential or potential difference (V)

$$R_{eq} = R_1 + R_2+ ... + R_n$$
$$V_{eq} = V_1 + V_2 + ... + V_n$$
$$I_{eq} = I_1 = I_2 = ... = I_n$$
$$R_{eq}$$ = equivalent resistance ($$\Omega$$)
$$R_n$$ = resistance of $$R_n (\Omega)$$
$$V_{eq}$$ = equivalent voltage (V)
$$V_{n}$$ = voltage of $$V_n$$ (V)
$$I_{eq}$$ = equivalent current (A)
$$I_n$$ = current through $$I_n$$ (A)
Circuits
In
Series
$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac {1}{R_2} + ... + \frac{1}{R_n}$$
$$V_{eq} = V_1 = V_2 = ... = V_n$$
$$I_{eq} = I_1 + I_2 + ... +I_n$$
$$R_{eq}$$ = equivalent resistance ($$\Omega$$)
$$R_n$$ = resistance of $$R_n$$ ($$\Omega$$)
$$V_{eq}$$ = equivalent voltage (V)
$$V_n$$ = voltage of $$V_n$$ (V)
$$I_{eq}$$ = equivalent current (A)
$$I_n$$ = current through $$I_n$$
Circuits
In
Parallel
$$B = \frac{\mu_o I}{2 \pi r}$$ B = magnetic field (T)
$$\mu_o$$ = vacuum permeability (H/m)
I = current (A)
r = distance (m)

$$F_B= qvBsin\theta = BIlsin\theta$$ $$F_B$$ = magnetic force (N)
q = charge (C)
v = velocity (m/s)
B = magnetic field (T)
$$\theta$$ = angle
I = current (A)
l = length (m)

$$\Phi_m = BAcos\theta$$ $$\Phi_m$$ = magnetic flux (Wb)
B = magnetic field (T)
A = area (m$$^2$$)
$$\theta$$ = angle

$$\mathcal{E}_{avg} = - \frac{\Delta \Phi_m}{\Delta t}$$ $$\mathcal{E}_{avg}$$ = average emf (V)
$$\Phi_m$$ = magnetic flux (Wb)
t = time (s)

$$\mathcal{E}=Blv$$ $$\mathcal{E}$$ = emf (V)
B = magnetic field (T)
l = length (m)
v = velocity or speed (m/s)

$$E=mc^2$$ E = energy (J)
m = mass (kg)
c = speed of light in a vacuum (m/s)

$$Q=mc\Delta t$$ Q = heat (J)
m = mass (g)
c = specific heat capacity ($$J/g ^\circ C$$)
t = temperature ($$^\circ C$$)

$$Q= m H_x$$ Q = heat (J)
m = mass (g)
$$H_x$$ = heat of fusion or vaporization (J/g)

$$Q = hA\Delta t$$ Q = heat (J)
h = heat transfer coefficient ($$W/m^2$$ $$^\circ C$$)
A = heat transfer area ($$m^2$$)
t = temperature ($$^\circ C$$)
Convection
$$Q = \frac {-kA\Delta t}{L}$$ Q = heat (J)
k = thermal conductivity ($$W/m ^\circ C$$)
A = heat transfer area (m$$^2$$)
t = temperature ($$^\circ C$$)
L = thickness (m)
Conduction
$$Q=Ae\sigma(t_1^4 - t_2^4)$$ Q = heat (J)
A = heat transfer area (m$$^2$$)
$$e$$ = emissivity
$$\sigma$$ = Stefan-Boltzman constant ($$5.67 \times 10^{-8}$$)
$$t_1$$ = temperature of radiator (K)
$$t_2$$ = temperature of surroundings (K)