# 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:

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. ### 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. ### 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. ### 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. ### 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. ### 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 :)

13. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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...

47. ### 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...
48. ### 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
49. ### 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...
50. ### 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!