What is Formulae: Definition and 139 Discussions

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:






{\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. M

    A New string formulae for Higgs mass and cosmological constant

    https://arxiv.org/abs/2106.04622 Calculating the Higgs Mass in String Theory Steven Abel, Keith R. Dienes [Submitted on 8 Jun 2021] There are at least two properties of the Higgs mass one might hope to explain with such a fundamental calculation: its criticality, and its participation in...
  2. ahbin98

    Heat Transfer Formulae for Charcoal-Concrete Experiment

    My experiment procedure is that I am using burning charcoal as the heat source, and there are three thermocouples used, first one measuring the temperature of the charcoal, second one measuring the inner temperature of the concrete block, third thermocouple is placed on the top part which is...
  3. M

    Question about Formulae for Motion in a Rotating Reference Frame

    Hi, I am reading the following question: "Particle P moves in a circular groove with radius ## a ## which has been cut into a square plate with sides of length ## l ##. The plate rotates about its corner ## O ## with with angular velocity ## \omega \hat k ## and angular acceleration ## \dot...
  4. M

    Describing recursive formulae in words

    I am only interested in the verbal descriptions of ##p_{n, 0}(4), \ p_{n - 1, 1}(3)##. The right hand side of ##p_{n, 0}(4)## describes the probability of choosing one ball from one jar and the probability of choosing one ball from another jar and the probability of one of the jars containing...
  5. SamRoss

    I Seeking better explanation of some quantum stats formulae

    In "Introduction to Quantum Mechanics", Griffiths derives the following formulae for counting the number of configurations for N particles. Distinguishable particles... $$ N!\prod_{n=1}^\infty \frac {d^{N_n}_n} {N_n !} $$ Fermions... $$ \prod_{n=1}^\infty \frac {d_n!} {N_n!(d_n-N_n)!}$$...
  6. E

    B Showing that formulae are invariant for all values in the domain

    I was just thinking about this and couldn't decide whether it was a silly question or not, so naturally I thought I might ask. It was partly prompted by one of the questions asked in the homework section. Every physical law I can think of is "self-correcting" if you substitute negative values...
  7. Benjamin_harsh

    Is my formulae correct for time of flight in this projectile problem?

    ##V_{oy} = V_{0}.sinθ = (20 m/sec)(sin 30) = 10 m/sec## ##V_{ox} = V_{0}.cosθ = (20 m/sec)(cos 30) = 17.3 m/sec## ##y = y_{0} + V_{oy}t - \large\frac {1}{2}\normalsize gt^{2}## ##0 = 50 + 10t - 4.9t^{2}## ##0 = 4.9t/6{2} - 10t - 50## ##t = \large\frac {-b±\sqrt {b^{2} - 4ac}}{2a}## ##t =...
  8. W

    How Does Conservation of Momentum Apply to Particle Decay?

    Attempt at solution: By conservation of momentum: $$P = (M,0,0,0) = p_1 + p_2 = (E_1 + E_2, 0, 0,0)$$ thus $$ M = E_1 + E_2 = 2k^2 + m_1^2 + m_2^2$$ Now $$E_1^2 - E_2^2 = m_1^2 - m_2^2 = (m_1 + m_2)(m_1-m_2)$$ $$ = M(m_1-m_2) = (2k^2+m_1^2+m_2^2)(m_1-m_2)$$ Isolating k: $$ k =...
  9. M

    When to use the adiabatic index in the polytropic process formulae?

    Hi, I was doing this question and I was slightly confused as to whether I ought to just substitute n = \gamma (the adiabatic constant) into the equation? The answers don't do this, but I was wondering why it was wrong for me to do so? This was only a small fraction of the question (which was...
  10. A

    MHB Calc Male & Female Cattle Pop Growth Rates: 30 Heifers, 100% Fert/Surv

    I want to estimate the number of male and female cattle produced over a period of time (say, five years and ten years) from an initial stock of 30 heifers, all 18 months of age at which age they are first joined (mated). Assume that the first calf is born when the mother is 27 months old...
  11. jamiebean

    The formulae for kinetic energy and Joules

    The formula for kinetic energy is 0.5x kg x v^2, where v= velocity The formula for joules is kg x v^2 I don't understand why does the difference exist and what is the difference between joules and kinetic energy isnt joule the unit for energy?? Thank you guys for helping me.
  12. Wrichik Basu

    Studying Is learning derivations of formulae always very important?

    I understand that it is useful to learn and remember the derivations of formulae in most cases. However, I tend to forget the derivations of several formulae, especially those in optics and dynamics. For a moment, let's forget the examinations. I wish to pursue higher studies in applied...
  13. T

    I Aesthetically pleasing formulae involving time?

    I sincerely hope that I'm posting this in the right place and without violating any etiquette. I've come here looking for opinions and suggestions from a community of people far more proficient in the field of physics than I am, with a topic that is probably a little unusual. The situation is...
  14. Math Amateur

    MHB Polarization Formulae for Inner-Product Spaces ....

    I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with the polarization formula for the complex...
  15. Math Amateur

    I Polarization Formulae for Inner-Product Spaces ....

    I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with the polarization formula for the complex case...
  16. D

    I Velocity Addition Formula: u_y > c?

    If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c. The relevant formula is: u_y = u_y'/(gamma * [1+v u_x' / c^2]) Apologies for formatting. Details: gamma = 1/sqrt(1-v^2/c^2)...
  17. R

    Momentum Formulae: Inertia & P=m*v

    I know that P=m*v but I saw that Momentum (p) =E/c how can we say this We need to have inertia to call the momentum of entity. Plzz solve this dilemma
  18. K

    Reduction Formulae Question : In= ∫x(cos^n(x))

    Homework Statement Let In = ∫x(cos^n(x)) with limits between x=π/2, x=0 for n≥0 i) Show that nIn=(n-1)In-2 -n^-1 for n≥2 ii) Find the exact value of I3 Homework Equations ∫u'v = uv-∫uv' is what I use for these questions The Attempt at a Solution Rewritten as ∫ xcos^n-1(x) cosx u'=cosx...
  19. N

    I Spin quantum numbers: correct names and formulae?

    I'm having trouble finding the correct names for the 4 standard labels: n, l, m, s. Where might I find, free online: their correct names (ie, no colloquialisms or short cuts) and the accepted formula for each (to be sure I use them correctly)? Thanks.
  20. Buggsy GC

    B Confusion over transposing formulae question

    Hello I'm working through transposing formulae of pearsons Anthony Croft and Robert Davidson's foundation maths 5th edition and I'm stuck on exercise 10.1 question 1)e) We're it states that I must transpose the formula to make x the subject. The formula is y = ¹/₂x and the answer x = ¹/₂y I...
  21. Zaent

    Is there software to simplify physics formulae?

    What I mean by this is that I'm looking to see if there's any sort of software out there that has formulae that it "knows" and can reduce/expand back and forth for you. A simple example would be that I type "I*R" and it gets simplified to "V" using this software, or vice versa. I understand...
  22. Clever Penguin

    B Deriving Special Relativity Formulae Steps

    I was bored, so I decided to derive the special relativity formulae. I drew the following diagram of a light clock: In order to find t, I did sinθ=d/ct Which gives tsinθ=d/c Which gives t=d/csinθ If v = 0, vt = 0, and θ = 90 sin90 = 1 t = d/csinθ = d/c We call this t0If v is greater than 0, vt...
  23. I

    Difference between the various COP formulae

    Homework Statement Homework Equations N/A The Attempt at a Solution My question is a simple one: how is the above equation for COPref different to the COPref equations I've already encountered (such as COPref = Qc/Win = (h1-h4)/(h2-h1). Is the above just a different form of these? Or is the...
  24. G

    I General formulae for the roots of a cubic equation

    Hi everyone. I'm sorry for the long thread. If you don't want to read all the introductory stuff I will mark the part towards the end where my questions are located. I'm trying to find the general formulae for the roots of the equation $$ax^3 + bx^2 + cx + d = 0$$ By using some changes of...
  25. tommowg

    Using Fresnel Formulae and Poynting vector problem

    Homework Statement I'm having a problem using the fresnel formulae for these two problems below: 1. Using Fresnel formulae and expression for the Poynting vector show that at the interface between two dielectrics in the absence of absorption R+T=1, where R – is reflectivity and T –...
  26. CheesyPeeps

    Resistance in Parallel Equation

    The formula to find the total resistance in a parallel circuit is 1/R=1/R1+1/R2+1/R3, but wouldn't it be easier to use R=1/(1/R1+1/R2+1/R3)? I've only ever seen the equation written like that once before, and I'm wondering if there's a reason as to why it's never really used?
  27. J

    Intro Physics Moving Beyond Formulae: How to Think Like a Physicist

    I am doing PHYS 172 at Purdue, modern mechanics which begins with algebra and introduces calculus. I am having a hard time seeing beyond a page of formulae and understanding physics as fundamental principles. The textbook is "Matter and Interactions" by Chabay and Sherwood, and I am also reading...
  28. H

    Euler's column Formulae application in aluminum cans?

    Maximum axial load is proportional to the second moment of area. Thus can we reason that aluminium cans are cylindrical because they have a high second moment of area(mr^2) compared to other shapes(Which gives it a higher max axial load.)?
  29. VoteSaxon

    Special Relativity derivations ....

    Homework Statement Using the special relativity formulae p = mv / [1 - (v/c)2] E2 = p2c2 + m2c4 derive linear relations between: (i) momentum and mass; (ii) energy and mass; (iii) energy and momentum, which involve only c, c2, β = v/c, and γ (= 1/sqrt(1 - β2)) The attempt at a solution I am...
  30. Z

    Different formulae for moment of inertia

    I know the formula for moment of inertia is but there are I = MR^2 but there are also formulae for different objects as shown in the picture. So, how and when do you use I = MR^2 ? Just in case of (a)? Thanks!
  31. S

    Damping coefficient formulae

    Hi, I have been looking for formulae for the damping coefficient, and I found two different formulae for it. http://www.xyobalancer.com/xyo-balancer-blog/viscous-damping-coefficient This webpage states that damping force, Fd is given by Fd=-cv, where c is the damping coefficient while v is the...
  32. S

    Bi Axial loading formulae rearranging help

    Homework Statement I need some help converting and rearranging the first formula to get the next formulas? As I need this for further reference, for a future assignment! Not homework![/B] Homework Equations Attached as thumbnails
  33. B

    Formulae for calculating the area of a quadrilateral non-cyclic

    I want knows if a formula for calculate the area of a quadrilateral non-cyclic needs of just four values (the values of the four edges) or if is necesseray 6 values (the values of the four edges MORE os values of the two diagonals)? This formula needs of 6 values (a,b,c,d,p,q): OBS: s =...
  34. K

    Cable rotations formulae or method

    Hello, and thank you for your time. I observed a wire vibrating is good at blocking things trying to pass through their area. for example a rope spinning around can stop a tennis ball thrown through that area. obviously the speed of the rope allows it to "protect" an larger area than its gauge...
  35. W

    MATLAB Converting Excel formulae into Matlab code

    Hi everyone, I will start off by saying that I am a complete novice in Matlab and prefer to use Excel however the data that I have requires more computing power than Excel can provide. I have 16 sets of data with over 70,000 rows and 9 columns. The first column is a time series separated into...
  36. binbagsss

    Parity formulae, orbital angular momentum, mesons

    So a particle has intrinsic parity ##\pm 1 ## . The parity of a system of particles is given by product of intrinsic parities and the result is: ##(-1)^l ## (1). Questions: 1) How does this result follow? and what exactly is ##l## here? so it's the orbital angular momentum, so say a particle...
  37. B

    Formulae with logarithmic terms

    Homework Statement w = 1/h ln(l/lo-1) w=-2.6, lo=16 and h =1.5 Find L. Homework EquationsThe Attempt at a Solution Plug in the values 2.6 = 1/1.5 ln(l/16 - 1) Make the log term the subject. ln(L/16 -1) = 1/1.5/-2.6 ln(L/16-1) = 0.666/-0.256 ln(L/16-1) = -0.256 Change the log statement to an...
  38. Medicol

    Possible formulae of an organic compound

    1. An organic compound containing 57.65% carbon, 4.21% hydrogen and 38.14% oxygen. Determine its possible organic chemical formulae in the form CxHyOz 2. There is none 3. I don't know
  39. K

    MHB Well formed formulae in Predicate Calculus

    Consider the following well-formed formulae in the Predicate Calculus: W1 = (∃x)(∃y) R(x, y) W2 = (∀x)(∀y) [R(x, y) ⇒ ∼ R(y, x)] W3 = (∀x)(∀y) [R(x, y) ⇒ (∃z)(R(z, x) ∧ R(y, z))] Prove that any model in which W1, W2 and W3 are all true must have at least 3 elements. Find one such model with 3...
  40. C

    A good MAahematical formulae book?

    Hi, I'm studying science (going from biology to molecular nutrition) and often find that I forget how to find solutions to graphs such as the quadratic formulae, or perhaps i forget the rules of Integrals Could someone recommend a good mathematical formulae/table book including derivatives...
  41. S

    MHB Reduction Formulae Application

    Can someone show me how I would "use" the reduction formulae for tan^n x ? I just want to see an example on when I would ever use it. A simple one will do.\frac{tan^{n-2}x}{n - 1} - \int tan^{n-2} x dx
  42. Q

    MHB Cylindrical Capacitor formulae- forming an intuition

    So far I have learned about Coulomb's law, the electric field, gauss's law, the electric potential and now capacitance. I feel that although I "know of" these topics, I don't actually "flow with them". Ignoring the math for a second; I want to form an understanding. And I think calculating the...
  43. Q

    MHB Deriving Y-Component of Uniform Electric Rod | E=-▽V

    This is essentially the problem. And this is what I did. Realizing the following: E = -▽V I simply took the derivative in regards to the vertical component, in this case "a". So: -dV/da [the above formulae] And I got the following: Κλl/(a sqrt(l^2+a^2)) Does that seem about right...
  44. F

    Help in rearranging a formulae

    Hi all, I was wondering if anyone could give me a hand in rearranging the following formulae to make v the subject? PAvail = 1/2 ρAv^{3}C_{p} This isn't for homework, its simply something I'm interested in and I would be immensely grateful to anyone who could do this for me. Oh and...
  45. S

    Predicate logic - true or false formulae

    Hello everyone, I can't seem to understand how to do this question. Determine whether the formula F: ∃x∀y(P(x) → x = y) is true or false under each of the following interpretations over the domain D = {a, b}. (i) both P(a) and P(b) are true; (ii) both P(a) and P(b) are false; (iii) P(a) is...
  46. DreamWeaver

    MHB Series acceleration formulae for common transcendental constants

    OK, so for starters, I'm not asking anyone to re-post results found in other books, papers, etc. That'd be entirely contrary to the basic idea of this 'ere thread. What I'm really interested in is this: have you - yes YOU, personally - found any new or presumably unique series acceleration...
  47. C

    Compton scattering, formulae question

    Homework Statement An X-ray source of wavelength gamma is directed at a sample; determine the maximum speed of scattered electrons.Homework Equations KE=(\gamma-1)mc2=hc/\lambda - hc/\lambda' The Attempt at a Solution I've been provided with the solution using the formula above, however it...
  48. P

    How to Design a Boolean Function for a Full Adder?

    Hi, Homework Statement I'd like to find Bθ:{0,1}3→{0,1}2 which is defined as follows: Input: x,y,z\in{0,1}, Output: s,c\in{0,1}, Functionality:2c+s=x+y+zHomework Equations The Attempt at a Solution I first tried listing all the possible combinations of x,y,z, and there are obviously 8. I noted...
  49. Alelin

    MHB EMF in Electric Guitars: Tutorial & Formulae

    Hi there i need a tutorial of how EMF works in an electric guitar and also which formulae is more suitable for solving EMF in the electric guitar thank u
  50. B

    Proving trig equations using addition formulae

    SOLVED! :) Homework Statement The question is as follows; Prove that (tan(A+B)-tanA)/1+tan(A+B)tanA = tanB Homework Equations I'm certain the addition fomulae need to be applied, although I'm not entirely sure how. I genuinely have tried many times! The Attempt at a Solution...