# Formula Definition and 55 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. ### I The probability density function for the double-slit experiment

I am desperate. I've scoured the web for the formula for the probability density function for the interference pattern obtained in the double slit experiment with both slits open. So I want to know the probability density function and not the intensity function. I prefer not to have references...
2. ### 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...
3. ### 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.
4. ### Formula for calculating the wavelength of sound in interference

Here is a diagram of experiment: Here is the results: Average distance between nodes (cm) Frequency (hz) Line 1 Line 2 Line 3 500 253 176 105 1000 333 438 None My analysis: ƛ/2=D ∴ƛ=2D where ƛ=wavelength (cm) D=distance between nodes/antinodes (the average,cm) 500hz: Line 1...
5. ### I Einstein aberration formula

Hello, everyone. I am trying to find an aberration of light formula in Einstein's writings that is given in terms of tangents. I did a fairly thorough internet search and all I could find was the formula he wrote in terms of cosines. Yet I have a vague memory that somewhere he did give the...
6. ### Electric Power - Which formula to use and when?

Homework Statement : [/B] If the length of the filament of a heater is reduced by 10%, the power of the heater: Options are- a) increases by about 9%. b) increases by about 11%. c) increases by about 19%. d) decreases by about 10%. Homework Equations : P[/B]=I2R Or P=V2/R Where P=power...
7. ### Charge Density Expression

Homework Statement A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere? Homework Equations Charge density ρ=dQ/dV Gauss's Law ∫EdA = E(4ϖr^2) The Attempt at a Solution If Q is uniform then ρ=Q/dV and the...
8. ### How can I calculate the maximum speed of a go kart?

Hello, I'm going to build a solar-powered go-kart. To determine the sprocket that I want to use I need a formula to calculate the top speed which also considers vehicle weight and other resistance forces. All the formulas I found just used sprocket tooth and rpm to calculate top speed but of...
9. ### Formula to calculate the charge in a sphere

1. The problem is: Which charge will a sphere have if it has a diameter of 0.26 meters and produces an electric field of 1030 N/C in the surface? 2. Gauss Law 3. I need the charge of the sphere but i couldn´t find any formula to calculate the charge given the distance (r) and electric...
10. ### What is water impact velocity formula?

Hello Everyone, I am brand new to this forum and I am currently doing "student research project task" where I need to conduct my own experiment basically. I am currently struggling to find a formula for an impact velocity. I hope there is someone in this forums that could help me. What I...
11. ### I Pauli principle and coupling term in Weizsäcker formula

Consider the pairing term in Weizsäcker formula. Here https://en.wikipedia.org/wiki/Semi-empirical_mass_formula#Pairing_term it is claimed that: I don't understand how Pauli exclusion principle should be the cause of this. This term comes from spin-spin interaction (or "coupling"), but I do...
12. ### Find the Initial Velocity and Launch Angle for a Particular Trajectory

Homework Statement Hello, so I’ve been trying to find some possible way to calculate this: The initial Velocity and angle needed to launch a projectile and reach the coordinates (x,y). The maximum height the ball can reach before it starts to head down to the target value should be y+5m The...
13. ### B Find the missing energy value given a set of data (Hypothetical question)

Hypothetical question: Let's say there's a granite cube with a volume of 60 cubic centimeters. A cannon ball is shot at it, reducing it to rubble, and the kinetic energy of the ball was 10,000 joules. We use the same ball with the same kinetic energy output on a stronger unknown substance with...
14. ### How to calculate voltage drop

So I have two formulas for calculating voltage drop. The first is: Vdrop = Vin * R1 / ( R1 + R2...). This let's me calculate the voltage drop on the first resistor in a series of 2 resistors. You can also extend this to more resistors in series just by summing all the resistors. However, I do...
15. ### How to measure the force generated by a tyre when it fails?

Hello everyone, I am trying to work out how much force is generated when a tyre fails at a certain pressure. The tyre will be inside an OSHA section 1910.177 compliant tyre cage. What calculation would be used to solve the following?: The tyre size is 35 x 11.5-17 with a rated inflation of...
16. ### I How to determine if an asteroid will burn up or hit Earth?

I want to make a interactive simulation that shows whether or not an asteroid will hit the surface of the Earth. It would have 2 sliders for you to control the speed and mass of the asteroid. The simulation will output "yes" or "no" if the asteroid hits the surface. Is there a mathematical...
17. ### Complex Numbers: Euler's formula problem

Homework Statement Homework Equations The Attempt at a Solution I attempted to use the formula zj = xj + iyj to substitute both z's. Further simplification gave me (x1 + x2)cosθ + (y2 - y1)sinθ or, Re(z2 + z1)cosθ + Im(z2 - z1)sinθ. Is this a valid answer? Or are there any other...
18. ### I Problem Hubble parameter

This is the time derivative to calculate the speed which a galaxy moves away from another galaxy. I don't understand how they get from da/dt (xi − x1) to (∙a)/a a(t). (xi − x1). Could anyone explain this? vi(t) = d/dt (ri(t) − r1(t)) = d/dt a(t)(xi − x1) = da/dt (xi − x1)...
19. ### B Convert from lux to candela

hello i'm working on a project that consist on reading the light of LEDs on PCB to determine the color code (R,G,B) and light intensity but the sensor gives me values in LUX which is the illuminance and i need to convert them to Candela I found this formula in wikipedia but i didn't understand...
20. ### B Not sure what this problem would be called....

Hi, I am trying to write a function which would take two arguments: -> number of bits (which are a binary 0 or 1 value) N -> and acceptable number of mismatching bits M The function would statistically determine the probability of having M or less mismatching bits when randomly generating two N...
21. ### How to find Kepler's law from Newton's laws

We were asked to do an experiment where we had to prove the equation: T2=(4π2m)/Mgr Where M is the mass of the mass stack in kg (0.3kg), m is the mass of the rubber bung in kg (0.0226kg), T is the time taken for one rotation in seconds, r is the horizontal radius of rotation in meters, and g is...
22. ### Help in understanding sum of torque equation

I've been reading my physics book and there they derived the formula ∑τ = Iα where τ is torque, I is moment of inertia of a rigid body and α is the angular acceleration. They did by taking an arbitrary particle on the rigid body with an applied external force tangent to the rotation. τ1 = Ftan *...
23. ### Formula from systematic name

Homework Statement Sodium chlorate(I) Sodium chlorate(V) Potassium nitride(III) Phosphorus(III) chloride Magnesium iodate(I) Homework Equations None The Attempt at a Solution I know the number in the bracket refers to what's before it, i.e. in sodium chlorate(V), the (V) means that the...
24. ### Glass fibre Aquarium pool minimum thickness?

Hello, I am working on a Project and it has been a while since i did calculations With mechanics. The pool would be made in glassfibre with polyester and will be: L=2000mm W= 1750mm h= 400mm we use the E-module for glass, so we use E= 70 000 N/mm2 I= bh3/12 = 2000mm x 4003 mm /12 = 1,067 x...
25. ### Thermodynamic problem and formula homework help

An ideal gas at initial state has temperature 300 K has been compressed under constant pressure of 30 Pa from volume 3 cubic meters to 1.8 cubic meters. In the process 75 J of heat was lost. A. Find the change in internal energy B. Find the final temperature I tried two methods in A and they...
26. ### Formula For Calculating Output Power of a Turbine

Good evening, This Conversation is in regards to questions i have of a project of mine. I am, in a sense, looking to make a generator of sorts, one that uses a magnetic tesla turbine in order to power an electric motor. Unfortunately, i am at a loss for what formula i would need to figure out...
27. ### Correct formula for induced voltage with a stationary coil?

I'm making an AC generator with a stationary coil and rotating magnets. What would be the correct formula to find induced voltage at a certain rotation speed (along with the units)? All sources I've found are either non-applicable or do not explain what units to use. Thank you for the help.
28. ### Corona discharge current formula

I'm trying to find a formula for the current flowing through a wire that is only undergoing corona discharge into air. The wire is connected to a charged sphere, which provides the voltage. So far, I've just found formulas for certain ionization coefficients and electric fields, but no current...
29. ### Stoichiometry: Identify the metal and formula of it

Homework Statement All of the lanthanide metals (La through Lu) react with HCL to form compounds having eithe the formula MCl2, MCl3, MCl4, (where M represents the metallic element). Each metal forms a single compound. A chemist has a 0.250g sample of a lanthanide metal, and she wishes to...
30. ### Magnetic Field outside an Iron Core Solenoid

I need help in calculating the magnetic field outside of an iron core solenoid at different distances. I have made an electromagnet by taking a 99.99% pure iron (5cm in length and 1 mm in radius) and wrapping wire over it. I have measured it's magnetic field at the end and cannot find an...
31. ### A Formula for calculating neutron flux?

I have a liquid scintillator, the electronics system, and a beam of neutrons from a reactor. How do I calculate the neutron flux? Cold anybody give me a formula or equation? Not this equation: phi = n X v, where phi - flux, n = number of neutrons per cm3, v = velocity of the neutrons, because I...
32. ### Rearranging a SUVAT Equation

Hello everyone, Please can someone help me rearrange this equation to make t the subject: Relevant equations: My attempt at a solution: Thank you all for you help
33. ### Calculation of torque of engine (mathematically)

We have tried to convert a petrol engine into a compressed air engine back in our graduation project. At that time we only measured the RPM of engine using tachometer and pressure of compressed air using pressure gauge. Now, we need to know the power of wngine at those readings. As the setup is...
34. ### Finding acceleration from distance and time

Homework Statement A bullet with a mass of m=15.5 g is shot out of a rifle that has a length of L=1.02 m. The bullet spends t=0.16 s in the barrel. Write an expression, in terms of given quantities, for the magnitude of the bullet's acceleration, a, as it travels through the rifle's barrel...
35. ### Formula for annuity payments

So, unless you've been living under a rock, you should know the jackpot for the powerball is at 1.5 billion dollars. I was looking up the distribution of annuity payments and the website said that the payments are not equally distributed. They are incremented by 5% each year. Like the nerd I...
36. ### The # of bright fringes in a double slit with finite width?

Homework Statement Laser light with a wavelength 633 nm is used to illuminate two slits separated by 0.125 mm. The width of each slit is 0.0150 mm. Assuming that only fringes between the first minima in the pattern are counted, how many bright fringes are visible? lambda = 633nm d = 0.125mm w=...
37. ### Why do we multiply permittivity of vacuum with relative permittivity?

Why do we multiply permittivity of vacuum with relative permittivity? What does this calculation mean?
38. ### Energy in a capacitor

why is the formula of energy in a capacitor E= C x U^2 /2 I understand it mathematically, but I do not understand it if you apply it to a real situation. Is there anyone who can explain that?
39. ### Acceleration due to gravity?

using Newtons equation for gravitational force one can fling that the acceleration due to gravity, g' above the surface of Earth as g' = g (d/(d+h)) but I find that there is a different equation for the same as g' = g ( 1- 2h/r ) I know the first formula is right but I can't doubt the...
40. ### Help with structural formula and absolute configuration

1. Complete structural formula, identify the absolute configuration of each asymmetric center (if it applies) Bond rotation may be necessary 2. Is the first one right? The second one which is Newman must be turned to boat and then I write it in the boat? The Attempt at a Solution : On the...
41. ### Formula of Solenoid Magnetic B-field at Ending, Middle and Outside

Can anyone way in on the correct Formulas of a Solenoid Magnetic B-field at Ending, Middle and Outside? I have the following so far but some of them seem to contradict one another . Photo #1: Photo #2: Photo #3: Photo #4: Photo #5: Photo #6:
42. ### Complex tangent formula proof

Homework Statement This is an easy one, but keep in mind I'm kind of a newbie, anyway I can't figure out how to get the next formula... tan(z) = (tan(a)+i tanh(b))/(1 - i tan(a)tan(b)) Homework Equations This is the third part of an excercise, previous I proof the follow, -all using the...
43. ### Distance to which magnets start attracting each other

Hi, I was wondering whether it was posible with a formula to measure the distance to which two equal magnets start attracting to each other. I was looking at this web page https://www.kjmagnetics.com/blog.asp?p=surface-fields-101 and I am not sure if this is the right formula. I have two...
44. ### Explanation of this popular t-shirt equation

Happened to pass someone wearing a t-shirt today with the logo: F/C^2(sqrt(-1))PV/nR Could you explain to me what this means? Thank you
45. ### Deriving formulas used for vectors in physics.

Hey guys and gals, I'm taking an online physics course just to kind of learn the basics before I take the real thing this summer. The course is from OpenYale for those interested (oyc.yale.edu). Anyways, the professor was talking about some formulas for finding ##\vec{r}(t) = r(i(cos\omega t) +...

Homework Statement log39x4 - log3(3x)2 The answer sheet says that the answer is 0, but when I work the problem both ways I get: 2log3x Any ideas? Homework Equations logxy/z = logxy - logxz The Attempt at a Solution Formula Sheet 20-30 Minutes of Messing around with the problem
47. ### Combined Gas Law

I am studying National 5 physics, and my exam is tomorrow. I need some last-minute help. I'm struggling a little bit with the combined gas law, P1V1/T1 = P2V2/T2, and I'm not sure why. It would help me a lot if you could show step-by-step how the formula is used. Thanks for your time, it's very...
48. ### Pressure of a sphere on a regular surface

Since the pressure a sphere exerts on a surface tends to infinity, how do you actually calculate it? My guess would be trying to see how many atoms of the surface (a straight line) and of the sphere collide. But this is very dependent on the materials and exterior factors. I have searched...