What is Formula: Definition and 1000 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. S

    How do I use LaTex in the forum for to write equations?

    Hello. I registered today. Maybe you can help me. How do I use LaTex in the forum for to write equations?
  2. Rageuke

    I Need help simplifying standard error formula for redshift

    SE = standard error, expressed as sigma(x) n = number of observations we take into account (from a total population) when calculating the standard error sigma-index-x = standard deviation N = total population x-index-i = element of that population mu = mean of the population -> filled in all the...
  3. Leo2024

    Optimal thin absorber of electromagnetic energy

    Hi, I am a material engineer and have a question about a formula derivation relative to microwave absorption. I really cannot figure it out after days of trying. This should be simple for a specialist. In this attached paper, how could one derive Eq(10) based on Eq (8) and (9)? Is k_2 in Eq...
  4. E

    Drag Coefficient -- What is the constant K?

    As I understand, the drag coefficient looks as follows: CD=CD0+CL/πAe however, the professor threw in a new constant, K, and I am having trouble understanding what this means. The formula now looks like this: CD=CD0+k1CL+k2CL^2 could someone help? Thanks!
  5. paulb203

    Solve using complete the square vs. quadratic formula

    Using the complete the square method I got; -3+root8 or -3-root8 But using the quadratic formula (to check my answer) I got; -3+root 10 or -3-root 10 I've checked both answers several times but can't get to the bottom of it :)
  6. T

    Understanding the Proper Uncertainty Formula to Use

    Good evening, I'm running into a little confusion on the second part of this problem due to finding two different formulas for calculating the uncertainty in multiplied quantities. The way that I was taught was something like this. If ##z = x \cdot y##, then: $$\dfrac{\delta z}{z} =...
  7. M

    I Help in understanding Eigenvectors please

    Hi; struggling a little with eigenvectors; I can get to the equation at the foot of the example but I can't understand the "formula" leading to the setting of x = 3 at the foot of the example? thanks martyn
  8. P

    Conceptual misunderstanding in applying formula for work done in adiabatic compression

    I was trying to solve a JEE ADVANCED 2020 paper 1 question 13 on thermodynamics. I attempted the problem and got a different answer than they did. I did it in a different way, but I can't find a mistake in both methods. So now I am stuck. I think the problem is in the first step probably using...
  9. D

    Projectile motion, initial height and range given, find initial velocity

    the answer to this question uses the above formula with the tangent function and solves for the initial velocity, i used the equation (v.sinθ^2) = (v.sinθ)^2 - 2gΔy, setting final velocity equal to zero and solving for initial velocity. this kinematic equation gives a different answer. can...
  10. M

    Mass on a spring from equilibrium

    Can someone explain that, when using the formula (Fs=1/2 kx^2) why do we use x=0.1m instead of 0.05m? Seems like a simple concept but why isn't it 0.05m (since 0.05m from equilibrium). Thanks.
  11. A

    Finding Gauge Pressure in this Manometer

    Hi everyone. I would like to ask how do you find the gauge pressure at point 4. I know the formula, which is: Pgage = Pabs - Patm But I don't know which one is the Pabs. This is my attempt: P4 = (600 kg/m^3 × 9.8 m/s^2 × 0.05 m) + Ptank This is all I can do. Please professors help me on...
  12. M

    I Contradiction in formula for motional EMF

    The formula for motional EMF is $$\oint({\bf{v}}\times{\bf{B}})d{\bf{l}}=-\frac{d}{dt}\int{{\bf{B}}\cdot{\bf{\hat{n}}}da}$$However applying this for a rotating disk of radius a there seems to be a sign contradiction $${\bf{v}}\times{\bf{B}}=\omega s{\bf{\hat{\varphi}}}\times...
  13. J

    Alpha particle close to the nucleus

    Hello everyone, while studying I found this task in my textbook. Solving this problem with the help of the formula seems quite straightforward. But I get a different result than the solution the textbook offers. I get: Around ##5∗10^{−15}m## (which is a typical solution for a radius of a...
  14. paulb203

    Changing the subject of a formula

    Step 1 Mult.both sides by 4+t; p(4+t)=3-2t Step 2 Expand brackets; 4p+pt=3-2t Step 3 Sub.4p from both sides; pt=3-2t-4p Step 4 Add 2t to both sides; pt+2t=3-4p Step 5 Factorise left side; t(p+2)=3-4p Step 6 Divide both sides by (p+2); t=3-4p/p+2 Nb. I did try an online...
  15. E

    What is the right formula to use in this context? (momentum conservation)

    First i think the correct solution to the problem is But my friends argue that it is not what i did , i am confused we didn't see the whole chapter on momentum in class, (Youtube thank you) here is what my friends say : (0.3×5) + 0 = (V×0.3)+(0.4×2) and they get they a final speed of 2.33...
  16. MP97

    B Rotational Kinematics -- questions about a=mg sin(theta) / (m+I/R^2)

    Hi, I am learning. Rotational Kinematics and I was given this formula in class: a=mgsin(theta)/(m+I/R^2); however, I couldn't understand the professor's explanation of where it comes from. Could someone provide some insights about it? I appreciate any help you can provide.
  17. al4n

    B I'm trying to find a general formula for a harmonic(ish) series

    Im looking for a general formula for the partial sum of a series where the nth term is in the form of a_n = 1/(c+kn), where c and k are arbitrary constants. it "looks" like a harmonic series but not in the form I'm capable of figuring out. help.
  18. Y

    LaTeX What do you use to write formulas here in Physics Forum?

    I was here over 10yrs ago, at the time, I use LaTex. You still using that today or there's something new? I am encouraging my grand daughter to come to this forum as she's going to college soon. I don't want to tell her to learn the wrong thing as it's been over 10yrs already. Thanks Alan
  19. Remle

    Doubt Calculating the Total Displacement for this Person Walking

    I having a little bit of problem with ##\Delta d = d_f - d_i##. When substituting fo ##d_f## and ##d_i##, should I follow the signs rule (positive or negative)? For example, The problem shows that the displacement is ##1.2~\rm{km}, south## by solving ##\Delta d = -2.5 + 1.3## and I get that, but...
  20. Euge

    POTW Projection Formula for Ringed Spaces

    Show that if ##f : X \to Y## is a morphism of ringed spaces, ##\mathscr{F}## is an ##\mathcal{O}_X##-module and ##\mathscr{E}## is a locally free ##\mathcal{O}_Y##-module of finite rank, then for all ##p \ge 0##, there is an isomorphism $$R^pf_*(\mathscr{F}\otimes_{\mathcal{O}_X} f^*\mathscr{E})...
  21. C

    Chemistry Understanding the concept of electron per shell

    Looking at Cacium for th electron arrangements according to shell numbers is 2, 8,8,2 since Cacium have four shells. Going by the formula 1st shell has:$$2n^2=2\times 1^2= 2 ~electrons $$ 2nd shell has:$$2n^2=2\times 2^2= 8 ~electrons $$ 3rd shell has:$$2n^2=2\times 3^2= 18 ~electrons $$ But...
  22. D

    What is the Resultant Force from adding these two forces?

    when is apply the formulae of resultant force for the two equations the angles cancel out and I can't get any value for the angle when i add the two equations: R^=f1^2+f2^2+2f1f2cos(theta) squart3*R=f1^2+f2^2-2f1f2cos(theta)
  23. Valour549

    Two ways of integration giving different results

    I am trying to do the double integral. And I remembered there's this formula that says if the integrand can be split into products of F(x) and G(y) then we can do each one separately, then take the product of each result. Taken from Stewart's Calculus 9E. So I tried to do the integral two...
  24. chwala

    Finding the projection of a Vector

    I am looking at this now; pretty straightforward as long as you are conversant with the formula: anyway i think there is a mistake on highlighted i.e Ought to be ##-\dfrac{15}{37}(i+6j)## just need a confirmation as at times i may miss to see something. If indeed its a mistake then its time...
  25. S

    Question about permutation formula -- How to use the formula when r = 0 ?

    ##P^5_0=\frac{5!}{(5-0)!}=1## But when I use ##P^n_r=n(n-1)...(n-r+1)##, I get ##P^5_0=5(4)...(6)## Where is the mistake? Thanks
  26. C

    Finding compound interest formula

    For this part (a), I got ##A(t) = 500 \times 6.5^t## where t is in years. Does someone please know whhy their function is to base e? Is it because the money is compounded continuously? Many thanks!
  27. C

    Deriving density formulae from first principles

    Can someone please help derive the relations below from first principles? Also does someone please know what happens when ##ρ_{object} = p_{fluid}##? Many thanks!
  28. Mohmmad Maaitah

    Deriving force from momentum using d(mv)/dt

    How did the d(mv)/dt become the other two? Can someone explain how do we derive for new formulas in physics?
  29. A

    I Probability to get a certain number or less by throwing two 6-faced die

    In a board game, I need to reach a certain place in a board divided into boxes, I move by throwing 2 six-faced dices. If my goal is 4 boxes away I need to obtain at least a combination of numbers that sums to 4, but any higher number is also a favorable outcome. I want to calculate the...
  30. J

    I Noise Proportional to Square Root of Illumination: Need Formula Help

    Many people have said that the noise that affects laser light is proportional to the square root of the illumination. But I can't find the formula. Can anyone help?
  31. M

    Racing car coolant formula ideas

    Hey guys! So, I’m working on an engine coolant for track motor sports that can’t contain any glycols. I think a simple “water wetter” will work. A surfactant such as Tydol X-100 come to mind along with an anti foaming agent and aluminum corrosion inhibitor. I know there are commercial...
  32. C

    Finding formula for nth derivatives of some functions

    For part(a), The solution is, However, I am having trouble understanding their finial formula. Does anybody please know what the floating ellipses mean? I have only seen ellipses that near the bottom like this ##...## I am also confused where they got the ##2 \cdot 1## from. When solving...
  33. Mr_Mole

    Rearranging formula using logarithms

    My attempt that doesn’t work. t=-RC ln(1-I/6.7)
  34. barryj

    I Formula for credit card balance as a function of payments

    I have been trying to find the financial formula that will give the balance of a credit card debt as a function of time. Example, at 18% interest, if I pay $150 a month how long will it take me to pay off my debt. When I google, I get pointers to Excello functions. I want to know the exact formula.
  35. J

    A Margules' Power Series Formula: Deriving Coefficients

    Margules suggested a power series formula for expressing the activity composition variation of a binary system. lnγ1=α1x2+(1/2)α2x2^2+(1/3)α3x2^3+... lnγ2=β1x1+(1/2)β2x1^2+(1/3)β3x1^3+... Applying the Gibbs-Duhem equation with ignoring coefficients αi's and βi's higher than i=3, we can obtain...
  36. FEAnalyst

    Beam deflection and curvature radius formula doubts

    Hi, I am working with leaf springs and studying the derivation of the formula for the deflection of such a structure. The derivation is shown here: My only doubt is how to obtain the following formula: $$\delta=\frac{L^{2}}{8R}$$ where: ##\delta## - deflection, ##L## - length of the beam...
  37. C

    Deriving general specific heat capacity formula

    For this, Dose anybody please know of a better way to derive the formula without having ##c = \frac{\Delta Q}{m \Delta T}## then taking the limit of both sides at ##\Delta T## approaches zero? I thought ##\Delta Q## like ##\Delta W## was not physically meaningful since by definition ##Q## is...
  38. brochesspro

    I Angular velocity of a rod and what formula to use while solving.

    The question is: A uniform rod of length ##L## stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What is the rod's angular velocity when it makes an angle of 30 degrees with the floor, assuming...
  39. V

    Cannot understand what ##(mod ~ \pi)## means in the given formula

    My understanding is that it probably means either ##+ \pi## or ## - \pi##, so that ##\pi## is either added to or subtracted from the first term, just like ##|x| = \pm x##.
  40. brochesspro

    I Meaning of the terms in the formula of the net external force

    The mathematical representation of the net external force on a system(obtained from Newton's second law) is ##\vec F_{net} = \frac {d\vec P}{dt}##, which is the rate of change of linear momentum of the system. If we substitute ##\vec P = m\vec v## into the formula for force and differentiate, we...
  41. angrymonks

    Building a physics formula database -- Help please

    I'm looking to compile a large online database of physics formulas*. I have yet to find any comprehensive "physics list" that isn't too domain specific or simply scalable. My attempt will be to build it here newtondb.com following and expanding on pldb.com. It will be built using a treebase...
  42. L

    Rearrange formula and work out phase angle

    so far i think Ip = 10 f = 1000hz struggling with the phase angle
  43. chwala

    Make ##x## the subject of the formula

    This was a good one; just thought i would share...of course i know this forum has smart people who may probably come up with a different approach...it took me a few minutes to figure out ...:frown:and then alas! saw the magic... ##\sqrt{\dfrac {x^2+15t-3}{x^2}}=5t## ...
  44. C

    Proof of angle in path difference formula for two slits

    For this I am trying to prove that angle theta between PQ and QO is equal to theta highlighted so that I know I can use theta is the path difference formula. I assume that the rays ##r_1## and ##r_2## are parallel since ##L >> d## My proof gives that the two thetas are equal, however I am...
  45. patric44

    What is the correct formula for the reduced Chi square?

    Hi all I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD : $$...
  46. brotherbobby

    A formula involving the sum of cosines of the angles of a triangle

    Problem Statement : The statement appeared on a website where a different problem was being solved. I got stuck at the (first) statement in the solution that I posted above 👆. Here I copy and paste that statement from the website, which I cannot show : Attempt : To save time typing, I write...
  47. C

    How to get the structural formula of C3H6CI2?

    TL;DR Summary: I only know how to solve the C3H6 which is a double bond, is it right or wrong? Reference: https://www.physicsforums.com/forums/chemistry.83/post-thread
  48. zachary570

    Chemistry Finding the molecular formula of an unknown hydrocarbon

    Hello, I am having some trouble finishing this problem from my textbook and would like some insight on the problem. We are looking for the molecular formula of a hydrocarbon. So, if we let x = number of C atoms and y = number of H atoms then we need to find ##C_xH_y##. From the problem...
  49. H

    Help is needed for converting units of a simple formula

    How would you convert a volume mixing ratio [m3/m3] to the units of [molecules/cm3]? The temperature is given to be 293K and the air density is 1 kg/m3. Please help!