General Science: 100+ Most Important Scientific Formulas

Question 1. What is the formula that relates mass to weight?
W = mg relates mass (m) to weight (W).

Question 2. What is the formula that relates mass to molar mass?
m = nM relates total mass (m) to molar mass (M). Note: n = number of moles.

Question 3. What is the formula for converting from Celsius to Kelvin?
TK = TC + 273.15 converts from Celsius to Kelvin. (Bonus for the decimals.)

Question 4. What is the formula for converting from Celsius to Fahrenheit?
TF = 9TC/5 + 32 converts from Celsius to Fahrenheit. Note: 9/5 = 1.8.

Question 5. What is the formula that relates force to pressure?
P = F/A relates force to pressure.

Question 6. What is the formula that relates density to pressure for a fluid?
P = dgh relates density to pressure for a fluid. Note: d = density. It is often written with the Greek letter rho:
Bonus if you added atmospheric pressure, P0, according to Pascal’s law.

Question 7. What is the formula that relates mass to density?
d = m/V relates mass to density. It is often written with the Greek letter rho:

Question 8. What is the formula for molarity?
M = moles of solute / liter of solution is the formula for molarity.

Question 9. What is the formula for molality?
m = moles of solute / kg of solvent is the formula for molality.

Question 10. What is the formula for percent error?
The formula for percent error is:
Note: E = observed, A = accepted.

Question 11. What is the formula for percent difference?
There are two common conventions for percent difference. One divides by the smaller value: The other divides by the average:

Question 12. What is the formula for the percent yield of a chemical reaction?
The formula for percent yield is:
(PY = percent yield, AY = actual yield, TY = theoretical yield)

Question 13. What is the formula for the percent composition of an element in a chemical formula?
The formula for percent composition (by mass) is:
(PE = percent element)

Question 14. What is the formula for the mass percentage of a component in a solution?
The formula for the mass percentage of a component of a solution is:
(MP = mass percent, CM = mass of component, TM = total mass of solution)

Question 15. What is the formula for the mole fraction of a component in a solution?
x = ni/n (x = mole fraction, ni = moles of component, n = total moles)

Question 16. What is the formula for an object that travels with constant speed?
v = d/t or d = vt is the formula for constant speed.

Question 17. What is a formula for uniform acceleration? (Bonus for two or three formulas.)
Equations for one-dimensional uniform acceleration include:
(The notation may vary, but pay careful attention to the t’s, 0’s, and squares.)

Question 18. What is the formula associated with Newton’s second law of motion?
The equation for Newton’s second law of motion is: F = ma, or force is equal to mass times acceleration.

Question 19. What is the formula associated with Newton’s law of gravity?
F = G(m1m2)/r2 is Newton’s law of gravity.

Question 20. What is the formula associated with Coulomb’s law?
F = k(q1q2)/r2 is Coulomb’s law.

Question 21. What is the formula associated with Boyle’s law?
PV = const. (or P1V1 = P2V2) along an isotherm according to Boyle’s law.

Question 22. What is the formula associated with Charles’s law?
V/T = const. (or V1/T1 = V2/T2) along an isobar according to Charles’s law.

Question 23. What is the formula associated with the ideal gas law? (Bonus for two formulas.)
PV = nRT or (P1V1)/T1 = (P2V2)/T2 according to the ideal gas law.

Question 24. What is the formula to find the magnitude of a vector from its components?
The magnitude of a (2D) vector is: It can be represented as, V = (vx, vy), where V is the vector. These are the parts of vectors generated along the axes.

Question 25. What is the formula to find the direction of a vector from its components?
The direction of a (2D) vector is: To describe the direction of the vector, we normally use degrees (or radians) from the horizontal, in an anti-clockwise direction.

Question 26. What is the formula that relates period to frequency?
f = 1/T (or T = 1/f) relates period to frequency.

Question 27. What is the formula that relates angular speed to speed?
Angular speed (omega) is related to speed (v) by: The relationship between angular speed and linear speed is given by the equation ω = V/r.

Question 28. What is the formula that relates speed to centripetal acceleration?
ac = v2/R relates speed to centripetal acceleration.

Question 29. What is the formula for the force associated with Hooke’s law?
Fr = –k(x–xe) is Hooke’s law. (We’ll accept Fr = –kx.)

Question 30. What is the formula for the potential energy stored in a spring?
PEs = ½k(x–xe)2 is spring potential energy. (We’ll accept PEs = ½kx2.)

Question 31. What is the formula for gravitational potential energy?
PEg = mgh is gravitational potential energy for a uniform gravitational field. Bonus if you also wrote PEg = –G(mem)/R for the general case (R is not squared).

Question 32. What is the formula for kinetic energy? (Bonus for rotational kinetic energy, too.)
KE = ½mv2 is kinetic energy. Rotational kinetic energy is:

Question 33. What is the formula that relates force to work?
If the force and angle are constant, force is related to work by:
More generally:

Question 34. What is the formula for power? (Bonus for two formulas.)
If work is done at a constant rate:
(Otherwise, P = dW/dt.)

Question 35. What is the formula for momentum? (Bonus for angular momentum, too.)
The equations for (linear) momentum and angular momentum are:

Question 36. What is the formula for impulse?
Equations for impulse include: Impulse-momentum formula J=Δp

Question 37. What is the formula that relates force to torque?
Force is related to torque by: A torque is the result of a force rotating about an axis

Question 38. What is the formula for wave speed? (Bonus for two formulas.)
Equations for wave speed include: v = f × \lambda - Where v the velocity of the wave - f is frequency of the wave - \lambda wavelength.

Question 39. What is the formula that relates radius to diameter for a circle?
D = 2R relates radius to diameter for a circle.

Question 40. What is the formula that relates radius to circumference for a circle?
The formula that relates radius to circumference for a circle is: C=2πr (where “r” represents radius)

Question 41. What is the formula that relates radius to area for a circle?
The formula that relates radius to area for a circle is: The area of a circle is pi times the radius squared (A = π r²)

Question 42. What is the formula for arc length for a circular arc?
The arc length for a circular arc is: Arc Length Formula (if θ is in degrees) s = 2 π r (θ/360°) | Arc Length Formula (if θ is in radians) s = ϴ × r | Arc Length Formula in Integral Form s= ∫ a b 1 + ( d y d x ) 2 d x

Question 43. What is the formula for the perimeter of a rectangle?
P = 2L+2W is the perimeter of a rectangle.

Question 44. What is the formula for the area of a rectangle?
A = LW is the area of a rectangle.

Question 45. What is the formula for the volume of a sphere?
The volume of a sphere is: V = 4/3 π r³ - The formula for the volume of a sphere is V = 4/3 π r³, where V = volume and r = radius. The radius of a sphere is half its diameter.

Question 46. What is the formula for the volume of a right circular cylinder?
The volume of a right circular cylinder is: The volume of a cylinder can be calculated using the formula V=πr2(h). When determining the volume of a cylinder, you are simply finding the area of the circular base shape and then multiplying this by the height.

Question 47. What is the formula associated with Ohm’s law? (Bonus for the power formula, too.)
Ohm’s law and the related power equations (one power equation is enough) are: The equation for electrical power is P=IV. Where P is electrical Power, I is current, and V is voltage. If you multiply power by time this will give you the total energy, which is generally given in kilowatt-hours. The power equation and the Ohm's law can be combined to produce P=V^2/R and P=I^2R.

Question 48. What is the formula for capacitance? (Bonus for the stored energy formula, too.)
Capacitance and the related energy equations (one energy equation is enough) are: E = ½ × C × V². Using the general formula for capacitance, C = Q / V, we can rewrite the capacity energy equation in two other analogous forms: E = ½ × Q² / C or E = ½ × Q × V.

Question 49. What is the formula for capacitors in series? parallel? Which is which?
1/Cs = 1/C1 + 1/C2 + … for capacitors in series. Cp = C1 + C2 + … in parallel.

Question 50. What is the formula for resistors in series? parallel? Which is which?
Rs = R1 + R2 + … for resistors in series. 1/Rp = 1/R1 + 1/R2 + … in parallel.
Note that the formulas for equivalent capacitance and resistance are “backwards” because V = Q/C has C “down” whereas V = IR has R “up.” That is, capacitance and resistance play “reciprocal roles” when solving for potential difference (but note that they aren’t “actual” reciprocals, since current and charge aren’t identical.)

Question 51. What is the formula for standard deviation?
The standard deviation:
Note that (N – 1) is inside the square root. Not all scientists and engineers use the same form of the standard deviation, so if you know a slightly different formula, it may be okay.

Question 52. What is the formula for half-life?
t½ = –(t ln2)/ln(N/N0) is the formula for half-life. Alternatively, you could separately use the formulas t½ = ln2/k = 0.693/k and ln(N/N0) = –kt, where k is the decay rate.

Question 53. What is a formula for simple population growth (where resources aren’t exhausted)?
N = N0ekt is a simple population growth model where k is the reciprocal of the time constant. It can alternatively be expressed as ln(N/N0) = kt. (Why did the sign change from Question 52 to 53? In Question 52, the sample size decreases over time, whereas in Question 53 the population increases over time.)

Question 54. What is the formula that relates the apparent brightness of a star to its luminosity?
In terms of luminosity (or power), the apparent brightness is: Luminosity is the rate at which a star radiates energy into space. Apparent brightness is the rate at which a star's radiated energy reaches an observer on Earth.

Question 55. What is the formula to convert from degrees to radians?
The conversion from degrees to radians is: The value of 180° is equal to π radians. To convert any given angle from the measure of degrees to radians, the value has to be multiplied by π/180.

Question 56. What is the formula associated with Wien’s displacement law?
Wien’s displacement law is: The black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.

Question 57. What is the formula associated with Stefan’s law?
Stefan’s law is: The amount of radiation emitted by a black body per unit area is directly proportional to the fourth power of the temperature.

Question 58. What is the formula that relates nuclear binding energy to mass difference?
E = mc2 relates nuclear binding energy to mass difference.

Question 59. What is the formula introduced by Planck to relate energy of radiation to frequency?
E = hf (or E = nhf) is Planck’s formula for the energy of radiation.

Question 60. What is the formula introduced by de Broglie relating momentum to wavelength?
The de Broglie relation is: As light exhibits both wave-like and particle-like properties, matter exhibits wave-like and particle-like properties. This nature was described as dual behaviour of matter. On the basis of his observations, de Broglie derived a relationship between wavelength and momentum of matter.

Question 61. What is the formula associated with the first law of thermodynamics?
The first law of thermodynamics is: where delta U is the change in internal energy, Q is heat, and W is work. In general
(for a simple system), which simplifies to dU = TdS – PdV when N is constant.

Question 62. What is the formula for specific heat capacity or molar specific heat capacity?
Specific heat: Q = mCV(T – T0) if V = const. or Q = mCP(T – T0) if P = const. molar specific heat: Q = ncV(T – T0) if V = const. or Q = ncP(T – T0) if P = const.

Question 63. What is the formula for latent heat?
Q = mL relates heat (Q) to the latent heat (L).

Question 64. What is the formula for enthalpy?
H = U + PV is enthalpy. Note: U = internal energy.

Question 65. What is the formula for a reaction’s enthalpy change in terms of products and reactants?
The enthalpy change for a reaction is: The enthalpy change of a reaction is roughly equivalent to the amount of energy lost or gained during the reaction. A reaction is favored if the enthalpy of the system decreases over the reaction.

Question 66. What is the formula for the Gibbs free energy?
G = H – TS is the Gibbs free energy. Alternatively, G = U + PV – TS.

Question 67. What is the formula that relates entropy to temperature?
dQ = TdS relates entropy to temperature. If T = const., then the formula for the change in entropy of a process can me expressed mathematically as ΔS=QT(JK) Δ S = Q T ( J K ) where Q is the the heat transfer and T is the temperature at which the process takes place.

Question 68. What is the formula that relates entropy to the number of microstates?
Entropy is related to the number of microstates by: The number of available microstates increases when matter becomes more dispersed, such as when a liquid changes into a gas or when a gas is expanded at constant temperature.

Question 69. What is the formula for (thermal) linear expansion?
The formula for (thermal) linear expansion is: Use the equation for linear thermal expansion ΔL=αLΔT Δ L = α L Δ T to calculate the change in length,ΔL.

Question 70. What is the formula for the efficiency of a heat engine?
e = Wout /Qin = 1 – |Qout|/Qin is the efficiency of a heat engine. Specifically for the Carnot cycle, the efficiency becomes eC = 1 – Tc/Th.

Question 71. What is the formula for the work done along an isobar?
W = P(V – V0) is the work done along an isobar (constant pressure).

Question 72. What is the formula for spectral lines involving the Rydberg constant?
The Rydberg equation for the spectral lines of hydrogen is: The hydrogen spectrum is an emission spectrum, the atoms get excited and transition to different energy levels. Niels Bohr can study these transitions. Again he gave a formula known as the Rydberg formula to calculate the wavelength of these spectral lines. 1/λ = RZ2(1/n12− 1/n2h).

Question 73. What is Drake’s equation?
N = RsfpneflfifcL is Drake’s equation.

Question 74. What is the formula that relates electric field to force?
Electric field is related to force by: The strength of an electric field E at any point may be defined as the electric, or Coulomb, force F exerted per unit positive electric charge q at that point, or simply E = F/q.

Question 75. What is the formula that relates electric field to the voltage between two plates?
Electric field is related to the voltage between two plates by: According to Coulomb's law, the same electric field between two parallel conducting plates depends on the electric potential or voltage of the two plates and the distance between the two plates. So, the electric field E=Vd E = V d where d is the distance between the two charged plates

Question 76. What is the formula for magnetic force? (Bonus for two forms of the formula.)
Equations for magnetic force include: F = qv × B. The force F is perpendicular to the direction of the magnetic field B. It also is perpendicular to the direction of the velocity v.

Question 77. What is the formula for time constant in an RC circuit? (Bonus for LR circuit.)
The time constant in an RC circuit is: For an LR circuit, it is: For L−R circuit, the time constant is equal to- The ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance.

Question 78. What is the formula for the period of an oscillating spring?
The period of an oscillating spring is: Mass on a spring - Where a mass m attached to a spring with spring constant k, will oscillate with a period (T). Described by: T = 2π√(m/k).

Question 79. What is the formula for the period of a simple pendulum?
The period of a simple pendulum (with a small amplitude) is: The period of oscillation is · directly proportional to the square root of the length of the pendulum.

Question 80. What is the formula for index of refraction?
n = c/v is the index of refraction.

Question 81. What is the formula associated with Snell’s law?
Snell’s law is: For light of a given colour and a given set of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.

Question 82. What is the formula for the Doppler effect? (Bonus for explaining the signs.)
The Doppler effect equation is:
Note: v = speed of sound.
• If the observer is heading toward the source, use + in the numerator.
• If the observer is heading away from the source, use – in the numerator.
• If the source is heading toward the observer, use – in the denominator.
• If the source is heading away from the observer, use + in the denominator.

Question 83. What is the formula for the range of a projectile launched from horizontal ground?
The range of a projectile is: if the final position and initial position have the same height.

Question 84. What is the formula that relates molarities for dilution?
MconcVconc = MdilVdil relates molarities for dilution.

Question 85. What is the formula for the golden ratio?
The golden ratio is: Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, {\displaystyle {\frac {a+b}{a}}={\frac {a}{b}}=\varphi } where the Greek letter phi denotes the golden ratio.

Question 86. What is the formula for the rate of a reaction of the form a A + b B —> c C + d D?
The rate of a reaction of the form a A + b B —> c C + d D is: The rate expression for the reaction is Rate=K[A]x[B]y

Question 87. What is the formula associated with the rate law for a A + b B —> c C + d D?
R = k[A]m[B]n is the rate law for a reaction of the form a A + b B —> c C + d D.

Question 88. What is the formula associated with Archimedes’ principle?
FB = mfg is Archimedes’ principle; FB = dfVg is fine, too. (Rho is commonly used in place of d for density.)

Question 89. What is the formula that relates focal length and image distance for a lens or mirror?
1/do + 1/di = 1/f relates focal length and image distance for a lens or spherical mirror.

Question 90. What is the formula for the magnification of a lens? (Bonus for two formulas.)
M = hi/ho or M = –di/do is the magnification of a lens (or spherical mirror).

Question 91. What is the formula associated with Heisenberg’s uncertainty principle?
Heisenberg’s uncertainty principle is: Heisenberg's uncertainty principle states that it is impossible to measure or calculate exactly both the position and the momentum of an object.

Question 92. What is the formula associated with Malus’s law?
According to Malus’s law: When completely plane polarized light is incident on the analyzer, the intensity I of the light transmitted by the analyzer is directly proportional to the square of the cosine of angle between the transmission axes of the analyzer and the polarizer.

Question 93. What is the formula for dipole moment?
p = 2aQ or p = dQ is the dipole moment, depending on whether you work with the full distance (d) between the charges or the half-distance (a). Note: d = 2a. If you wrote instead, this merits credit.

Question 94. What is the formula for the height of a meniscus?
The height of a meniscus in a cylinder is: For a spherical me- niscus with θ = 0, the meniscus height zm = z(r) − z(0) is equal to the tube radius r. For water at 25 C, the numeri- cally calculated meniscus heights deviate less than 1% from r for radii < 0.5 mm while the deviation is larger than 10% for radii > 2 mm.

Question 95. What are the formulas for pH and pOH? (Bonus for three formulas.)
pH = –log[H+], pOH = –log[OH–], and pH + pOH = 14 (at room temp.).

Question 96. What is the formula for the speed of a P wave or S wave? (Bonus for both.)
The formulas are: The velocity of a P wave can be expressed as: Velocity P wave = ((B + 1.3G)/Density)1/2, where: B = the bulk modulus - the resistance to change in volume. G = the Shear modulus - the resistance to change in shape.
P wave α 2 = λ + 2 μ ρ | S wave β 2 = μ ρ

Question 97. What is the formula for seismic moment?
The formula for seismic moment is: Seismic moment can be defined as (6)M0=μAfD¯=2μES/Δσwhere μ is the shear modulus of the crust, Af is the rupture area of the fault, D¯ is the coseismic displacement averaged over the rupture area, Δσ is the static stress drop averaged over the rupture area, and ES is the radiated seismic energy.

Question 98. What are the formulas for capacitive and inductive reactance?
The formulas for capacitive reactance and inductive reactance are: The capacitive reactance is found directly from the expression in XC=12πfC X C = 1 2 π f C . Once XC has been found at each frequency, Ohm's law stated as I=V/XC I = V / X C can be used to find the current at each frequency. XC12πfC16.28(60.0/s)(5.00μF)=531Ωat60Hz.

Question 99. What is the formula for the phase angle for an RLC circuit with AC current?
The phase angle for an RLC circuit with AC current is: The phase angle in an RLC series circuit is determined by the source frequency. The capacitor dominates the impedance at extremely low frequencies, and the phase angle is around$ - {90^o}C$. The inductor dominates the impedance at very high frequencies, and the phase angle is approaching$ - {90^o}C

Question 100. What is the formula associated with the Compton effect?
The Compton effect equation is: 4 λ 1 − λ 2 = h m 0 c ( 1 − cos ⁡ θ )

Question 101. What is the formula for the photoelectric effect involving the work function?
K = hf – W for the photoelectric effect.

Question 102. What are the formulas associated with the Hardy Weinberg law?
p + q = 1 and p2 + 2pq + q2 = 1 for the Hardy Weinberg law.

Question 103. What is the formula for time dilation?
The formula for time dilation is: Δ t = Δ t 0 1 − ( v c ) 2.

Question 104. What is the formula for length contraction?
The formula for length contraction is: Length contraction L is the shortening of the measured length of an object moving relative to the observer's frame. L=L0√1−v2c2.

Question 105. What is the formula for chi-squared?
The formula for chi-squared is: χ² = ∑(O_i– E_i)²/E_i, where O_i = observed value (actual value) and Ei = expected value
Note: (O_i – E_i)² = (E<sub>i/<sub> – O_i)2. Why? Since O_i – E_i = (–1)(E_i– O_i) and since (–1)² = 1.

Question 106. What is the formula for porosity?
Porosity is: The percentage of void space in a rock. It is defined as the ratio of the volume of the voids or pore space divided by the total volume.

Question 107. Describe or write down Schrödinger’s equation.
Schrödinger’s time-independent equation in 1D is: When the potential energy is constant in time we can simplify the wave equation. We assume that the spatial and time dependencies of the solution can be separated, i.e. iℏ1ζ(t)ddtζ(t)=−ℏ22m1ψ(x)d2dx2ψ(x)+V(x).

The left-hand side is the Hamiltonian operator acting on the wave function. The left-hand side includes both kinetic and potential energy, while the right-hand side includes the total energy. Solving for the wave function allows us to predict various probabilities in quantum mechanics. For credit, at a minimum you should have noted that the wave function is involved and described the significance of the wave function, and how the equation relates to energy (but if you have knowledge of differential equations, for credit you should have been able to write the equation).

Question 108. Describe or write down Maxwell’s equations. 
There are four equations (in integral or differential form): is Gauss’s law, that the net electric flux through any closed surface is proportional to the charge enclosed by the surface. reflects that no magnetic monopole has been discovered. is Faraday’s law, that a changing magnetic flux through a loop of wire induces an emf in the loop of wire. Then there is Ampère’s law (including Maxwell’s addition of the displacement current), that the circulation of magnetic field through any closed loop is proportional to the current enclosed by the loop.

Question 109. What is the Arrhenius equation?
The Arrhenius equation is: (which may alternatively be expressed using Boltzmann’s constant instead of the universal gas constant).