Formula Definition and 1000 Threads

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.
The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula(often referred to as a well-formed formula) is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius:




V
=


4
3


π

r

3




{\displaystyle V={\frac {4}{3}}\pi r^{3}}
.Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic, analytical or in closed form.In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O−3 denotes an ozone molecule consisting of three oxygen atoms and a net negative charge.
In a general context, formulas are a manifestation of mathematical model to real world phenomena, and as such can be used to provide solution (or approximated solution) to real world problems, with some being more general than others. For example, the formula

F = mais an expression of Newton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.
Expressions are distinct from formulas in that they cannot contain an equals sign (=). Expressions can be liken to phrases the same way formulas can be liken to grammatical sentences.

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  1. D

    I Curious formula for elliptical polarisation

    Recently, I have been playing with polarisation microscopy and the measuring of elliptical polarisation. Standard treatments, like that in Born and Wolf, are usually a mayhem of all kinds of trigonometric functions. Now I derived a nice relation, which I didn't find in literature, although I am...
  2. guyvsdcsniper

    Finding acceleration from position formula

    I am trying to follow the solution to the following problem, both linked in the attachment. When trying to find the acceleration, a, that should be taking the derivative of r, the position formula twice. When doing so I get v = -ksinθ and a = -kcosθ. The attached work shows v being -(ksinθ)θ'...
  3. C

    I Equivalent formula for a Sound wave in a medium like an EM wave

    1.) In electromagnetics, wavelength in a medium is $$\lambda = \frac{\lambda_{0}}{n}$$, where $$n$$ is the refractive index. What is the equivalent formula for sound wave in a medium? 2.) Is there a reference sound velocity, like electromagetic wave speed in vacuum is $$c_{0} =...
  4. B

    I Resonant Frequency Formula for a given object

    I know the v = λf is the formula to find the resonance frequency of a single continuous wave and the formula for resonance frequency of a spring is: 1/2π∗sqrt(𝑘/𝑚) but what about the Formula for a random object? a car, or a rock, water ? is there one Formula to rule them all? or do you...
  5. Perchaddition

    B Can I use the circle circumference formula for a sphere?

    Trying to calculate a circumference of a sphere from a radius of 3.09 inches. Is 19.4 a correct answer? Just ran numbers in the first circumference calculator I found http://calcurator.org/circumference-calculator/. Can I use the same formula for a sphere? What can I say ...Geometry is not my...
  6. S

    MHB Rearranging Formulas: Finding W in Terms of M and L

    Hi, I have a formula which I need to rearrange but it's been a while since I covered this at school, I've tried to read up and re-study but I keep getting confused about what I can/can't do to the various brackets. The formula is: M = (((W x L / 2) x (L / 2)) - ((W x L / 2) x (L / 4))) I'm...
  7. B

    B Alternative elastic collision formula / physical interpretation

    Standard formula for final velocities ##v_1##, ##v_2## in elastic collision with masses ##m_1##, ##m_2## and initial velocities ##u_1##, ##u_2## is given by $$v_1 = \frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2$$$$v_2 = \frac{2m_1}{m_1+m_2}u_1+\frac{m_2-m_1}{m_1+m_2}u_2$$. By rearranging...
  8. warhammer

    I Guidance Requested on Inductance Formula for Solenoid

    In my textbook on EM, the formula for self inductance of a finite solenoid is given as: L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid. I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and...
  9. stuartsjg

    I Compressible choked gas flow through an orifice -- Excel formula

    Hello, I normally get these things working but I am a bit stuck as i don't feel I am getting sensible answers... The problem is simple (!): Q: Model the flow through an orifice with an upstream/supply pressure of 301BarA where the downstream pressure is in the range 1BarA to 301BarA. The...
  10. C

    I What is this formula measuring error?

    Variance and standard deviation and other measures of error I understand. This formula doesn't behave well for data sets centered around zero and also has other problems, like scaling differently as N increases than the standard deviation or standard error. Does anyone recognize this and can...
  11. Nikkki

    I Equation for circle points in 3D

    Hello, I am trying to solve a problem and I would like to ask for help. I have 3 points (A, B, C) in 3D space that are assumed to be on a circle. EXAMPLE 1 EXAMPLE 2 My goal is to create an algebraic formula to calculate the coordinates for 10 points on a circle composed of ABC points at...
  12. warhammer

    I Correct Formula for "No Fringe Condition" (Michelson Interferometer)

    In two different textbooks, there are two different formulas with different derivation styles for the "No Fringe Formation" Condition. In approach (a), they use an amalgamation of bright and dark for 2 wavelengths having very minute difference in the following manner: 2dcostheta=n*λ(1)...
  13. P

    Bethe formula dependence on charge of the material

    I think that it is a trick question and that the answer is that given dependence does not exist. Could anyone tell me if I am right?
  14. A

    Is the molecular formula for sugar correct?

    Is the following molecular formula for Sugar can be written as H22C12O11 or O11C12H22 or O11H22C12 or C12O11H22 or H22O11C12 instead of C12H22O11? Logically they can be written as mentioned above? If Not, Why? There can be many more examples similar to above.
  15. S

    Derivation of single slit diffraction formula

    I want to ask several questions regarding to the text: 1) Why do we find the minima of the diffraction? Why not the maxima?2) "Figure 25.32b shows two rays that represent the propagation of two wavelets: one from the top edge of the slit and one from exactly halfway down" Why do we take point...
  16. Father_Ing

    Torque formula derivation for a particle moving in circular

    Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)
  17. L

    Gravitational force - I translating the wording into the formula

    i spoke to my proffesor about it but all he said was to put 1 in m1 and m2... for r^2 since it says to quadruple to just put 4^2 I asked about the G in the equation but he said not to worry about iit and pretend its not there...
  18. Goinger

    I Wire Tension Formula: Shape Expression w/ 3 Pivots

    If the wire is bent by three pivots, I want to find an expression that represents its shape. There will be tension of wire and other physical factors. How can it be expressed?
  19. T

    Cauchy's Formula for Stress tensor

    Hello I am reviewing the proof of Cauchy's formula for the stress tensor and surface traction. Without exception, every book I look at gets to the critical point of USING the projection of a triangle onto one of the three orthogonal planes. However, I have never seen this proven. I have...
  20. Kairos

    I Classical Aberration Formula: Understanding & Application

    I believe I have understood the formula of aberration of light ##\tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} \sqrt{1-\beta^{2}} ## but I wonder if the non-relativistic formula ## \tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} ## has a physical relevance. Does this...
  21. A

    Semi empirical mass formula derivation help

    Can somebody please derive for me an example of the Binding energy from the Semi Empirical mass formula? I am trying myself but always there is a difference between the database binding energy and my own result. I am calculating the BE of Niobium 93. For the mass formula I used the coefficients...
  22. Boltzman Oscillation

    B Deriving formula for force by thought experiment

    Hi all, I was thinking punching a round ball on a flat surface and seeing how I could determine a formula for force from it. I thought the following: 1. The ball will go further the harder I punch and thus force must be proportional to displacement d. 2. Ball will go further if it is lighter...
  23. W

    Controlled chemical pressurization formula

    I have spent years physically charging high pressure bottles with multi staged bicycle pumps and spent large sums of money on electric high pressure air pumps not unlike a scuba tank air compressor. Pressure’s can be as high as 4500 PSI . The pressurized bottles are usually 300 to 500 cc’s. I...
  24. K

    I Possible simple formula for ellipse circumference

    While fighting a CAD program, today, I might have stumbled on a potential way to easily calculate the circumference of an ellipse. I checked my method against a half a dozen online ellipse calculators and while my formula gives different results, I can't see where I'm making any logical errors...
  25. maistral

    I Differentiation formula: Is this a typo?

    Red arrows. The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?
  26. M

    I Formula For Calculating Field Angle (Beam Angle) of Light?

    There are actually several questions. The formula for calculating the "beam angle" of light (emitted from lights bulbs, flashlights etc) is - α = 2 arcCos ( 1 - Lm ÷ ( 2 π Cd )) Where, α = beam angle in degrees Lm = luminous flux (Lumens) Cd = luminous intensity (Candela) The above formula...
  27. C

    Capstan equation, Euler's formula, power law friction

    Dear colleagues, I am dealing with rope friction and the so-called Capstan equation. Situation: A rope wraps around a cylinder with a wrap angle. It depends on the input force. There are very comprehensive approaches by other colleagues, where the friction value depends on the normal force or...
  28. alwaystiredmechgrad

    I Defect concentration formula w/o Stirling approximation

    In many cases, the concentrations of defects or charges are quite big enough to use SA, due to a big number of Avogadro's number. The derivation for the well-known formula of a defect concentration is followed. If the n_v is expected to be lower than 1, then it would be impossible to use SA...
  29. S

    I Analytical formula for the number of patterns by using combinations?

    A 4×3 matrix which has all elements empty, now I select any two consecutive elements until all elements are selected. I assign an index number (1 to 12) to the matrix element, in one row there are only 1,2,3 elements and 3 & 4 are not consecutive. for example, if I select index 1 & 2 of the...
  30. P

    A Gravitational Quadrupole Formula: Polarization Tensor

    In "Gravitational radiation from point masses", by Peters & Mathews, http://gravity.psu.edu/numrel/jclub/jc/Peters_Mathews_PR_131_435_1963.pdf, the emitted power from gravitatioanal quadrupole radiation per unit solid angle ##\Omega## is given by: $$ \frac{dP}{d\Omega} = = \frac{ G} {8 \pi c^2...
  31. Dukon

    A Kerr Metric Time Dilation Formula: Deriving Absolute Form

    Just as the time dilation formula for the Schwarzschild metric in terms of the position ##r## away from center of mass for a gravitational body and the Schwarzschild radius ##r_s = {2GM}/{c^2}## is given by $$ \tau = t \sqrt{1 - \frac{r_s}{r} } $$ so I'd like to know the corresponding...
  32. adan

    Construct a mathematical formula

    Hello, I have been thinking of it for a long time, and I would appreciate suggestions from math experts. I am working on a simulation of human agents. I want to set up a formula that defines the consumption probability (0,1), which consists of X, a value between 0 and 1, and two positive and...
  33. T

    A Adjusting Parameters for Identifying Features of an Action Potential

    I want to find a formula for an action potential (illustrated with the curve in the attachment). I would like to use the formula to graph this in Desmos graphics calculator. I don't have much of a math background, but a sine function comes to mind...I would like to get the precise shape though...
  34. L

    Chemistry What is the Correct Formula of the Metal?

    I haven't gone into a solution cause I found this question confusing
  35. appmathstudent

    I Rodrigues' Formula for Laguerre equation

    This is exercise 12.1.2 a from Arfken's Mathematical Methods for Physicists 7th edition :Starting from the Laguerre ODE, $$xy''+(1-x)y'+\lambda y =0$$ obtain the Rodrigues formula for its polynomial solutions $$L_n (x)$$ According to Arfken (equation 12.9 ,chapter 12) the Rodrigues formula...
  36. P

    I Unveiling the Proof of Induced EMF Formula: E = ∫ (v x B) · dl

    Why is ##E = \int (\vec v \times \vec B) \cdot d \vec l##? This seems to be a general formula, and I would like to know its proof. Thanks for all the help.
  37. Samkiwi

    How is the Relativity Formula Proven for an Electron in an Electric Field?

    It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other. Here's the questionA possible expression of speed as a function of time is the following: $$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A...
  38. Samkiwi

    Deriving and Verifying the Relativity Formula for Electron Speed

    It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other. Here's the questionA possible expression of speed as a function of time is the following: $$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A...
  39. L

    A $S^+$ and $S^{-}$ operators formula

    For ##\hat{S}^+## and ##\hat{S}^{-}## operators for any given spin ##S## relation \hat{S}^+|S,m \rangle=\sqrt{S(S+1)-m(m+1)}\hbar|S,m+1 \rangle \hat{S}^-|S,m \rangle=\sqrt{S(S+1)-m(m-1)}\hbar|S,m-1 \rangle Can someone please explain how we get those factors ##\sqrt{S(S+1)-m(m+1)}\hbar## and...
  40. PandaKitten

    Estimating the energy of an alpha particle using Bethe's formula

    The question is below. I tried reasoning that because x is constant, E is also constant however that gives me values in the range of 10^51. Then I tried to use numpy's ivp_solve function to solve the differential equation however I wasn't able to get that working either. Apparently I'm meant to...
  41. H

    Explaining a Physics Formula in Non-Physics Terms: Answer B

    According to the equation, the answer is B. Since the lecture didn't cover much about it, can someone explain this formula in a less physics way? Thanks.
  42. alya

    Help Needed: Deriving Formula for Computer Undergrad's Final Project

    My mentor wants the derivation of this formula. Me a computer undergrad, unable to figure it out, and my final project are on a halt due to this, any help from the community is greatly appreciated!
  43. V

    Deriving a formula for Kinetic Energy

    I have no idea how to do this. I've tried conservation of mechanical energy and it didn't work. Ek = Kinetic Energy R = horizontal range of the ball h = height from which the ball is released
  44. A

    MHB I need a formula how to calculate it

    A bag has identical balls of these colors: 1 white, 6 red, 9 green, and 3 purple. Without looking, a ball is drawn from the bag. You would most likely get a a. green ball b. purple ball c. red ball d. white ball
  45. ILoveParticlePhysics

    Does anyone know the formula to find the angle after a collision?

    I think it has to do with conversation of momentum and projectile motion.
  46. T

    Can someone tell me what "Value" means in this formula please?

    Hello. I am reading through a solar farm paper and I am getting a bit confused at looking at this formula: When it says "Value", I am guessing it refers to the cost of electricity per kWh? If that is the case, I wonder how many kWh are 18.4p/kWh?
  47. bhobba

    B Simple Derivation Of Euler's Formula And Applications

    Here is a simple way to get Euler's relation for those learning pre-calculus/calculus, so the trigonometric addition formula and the derivative of sine and cosine are easy. We will assume some basic knowledge of complex numbers and properties of Euler's number, e. Consider a small segment of...
  48. A

    Engineering Finding the parallel resonance formula

    Hello! I'm having trouble with getting the right result in this litle example. Consider this admittance $$ C + Cs - w^2_{pr} CCs $$ Now to get the resonance we need to set the imaginary part of the admittance 0.I did that like this $$0 = C + Cs - w^2_{pr} CCs $$ Now I need to get ## w^2 ##...
  49. ddedeasx

    How do you read the Brewster angle formula / equation?

    So far all I know is that n1 and n2 represent the refractive indices of the two media, and so is theta (I think). Please help
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