Formulas

1. Formula to Calculate Percentage

Percentage = (Value ⁄ Total Value) × 100

Example 1: There are 40 people in the room and room capacity is 100 people. Find how many percentage of room used?

Solution:-

Total People capacity of the room=100 people

Actual people in the room:-40

% used in the room :-( 40/100X100) =40%

Example 2: The exam paper is 100 marks and student marks is 55 marks out of 100.Find out the percentage of marks.

Solution:-

Total Examination marks=100

Obtained marks = 55

% of obtained marks = (55 ⁄ 100) × 100 = (5500 ⁄ 100) = 55%

2. Cos² theta formula

Formula: Cos ² theta= 1 – sin² theta

Example:-Find the value of cos square x, if Sin x=2/3 by using formula Cos ² theta= 1 – sin² theta

Solution: Cos ² x = 1 – Sin² x

= 1 – (2/3)²

= 1 – 4/9

= (9 – 4) /9

= 5/9

Cos x =5/9

 

3. Formula for circle area

Using following formula we can easily find the circle area. This formula will help to find circle area from given radius. If area is given then we can find the radius of the circle.

A=πr²= πd²/4=Cxr/2

Here,
r is the radius of the circle.
d is the diameter of the circle.
C is the circumference of the circle.

Example: Find the area of the circle whose radius is 4 cm using equation A=πr².

Solution:-

Here,

Radius of a circle = r = 4 cm

Area of a circle as per equation

= π r²

= π × 4² cm²

= π × 16 cm²

= 50.24 cm²

 

4. Calculate simple interest and compound interest using formula.

Explanation:-The simple interest is used to count the interest on invested or borrowed amount. Simple is generally applied on short term loans. Compound interest is sometime called interest on interest.

Formulas:-

1. Simple interest formula:-Principal amount x Rate of interest X Period       2.Compound Interest: - Principal amount (1 + Rate) ^Time – Principal amount.

Example: - Mahesh borrowed 5000rs from Ramesh for 2 years with 2% interest rate, how much simple and compound interest Mahesh should pay to Ramesh after two years?

Solution:-

Simple interest:-Principal amount * Rate of interest * duration    

⇒ Simple Interest = 5000 × (2 ⁄ 100) × 2

⇒ Simple Interest = 200rs

 Mahesh will pay 200rs simple interest on 5000rs after two years.

Compound Interest: - Principal amount (1 + Rate) ^Time – Principal amount.

⇒ Compound Interest = 5000 × (1 + 2 ⁄ 100)² – 5000

⇒ Compound Interest = 202rs

Mahesh will pay 202rs compound interest on 5000rs after two years.

5. Decimal number notation method.

Learn how to read decimal number by following method and count. This document help students to learn number method easily.

Number	Name	How many
0	zero
1	one
2	two
3	three
4	four
5	five
6	six
7	seven
8	eight
9	nine
10	ten
20	twenty	two tens
30	thirty	three tens
40	forty	four tens
50	fifty	five tens
60	sixty	six tens
70	seventy	seven tens
80	eighty	eight tens
90	ninety	nine tens

6. Example 2:-Explain the absolute value formula using example

Formula:-

|x|=a

|x|={x    x≥0, x    -x< 0}

Problem: Find the absolute value using formula 2 | x – 2 | = 32.

Solution:-

4 | x – 2 | = 32
| x – 2 | = 8
x – 2 = 8 or x – 2 = – 8
x = 8+ 2 or x = – 8 + 2
x = 10 or – 6

7. Density is the denseness of the material per unit area.

 

  Formula: - Density =mass /volume

Density unit is kg/m³

Example: - If given mass is 100kg and given volume is 10m³, calculate the density

Solution:-Here mass is 100kg and volume is 10m³

                So Density =mass/volume

                                  =100kg x 10m³

                                  =1000kg/ m³

 

8. Gross profit and loss calculation formula

Gross profit=Cost of sold goods-Cost of goods

Example:-If the material cost is 10 INR and sold value is 12 INR.Find the gross profit.

Solution:-

Here material cost is 10 INR

And sold value is 12 INR

So equation is Gross profit = Cost of sold goods-Cost of goods

Gross profit =12-10=2 INR.

Example:-If the material cost is 100 INR and sell value is 150 INR. Find the gross profit.

Example:-If the material cost is 100 INR and sell value is 150 INR.Find the gross profit.

Solution:-

Here material cost is 100 INR

And sold value is 150 INR

So equation is Gross profit = Cost of sold goods-Cost of goods

Gross profit =150-100=50 INR.

 

9.Force: Force is cause of motion or mass of objects multiplied by its acceleration

F=ma

F=Force

m=Mass

a=Acceleration

Example 1:- An apple is falling out from the tree. Consider apple weight 0.20Kg and gravity of the earth is 9.80m/s².What is the force acting on the gravity due to the gravity?

F=ma

Here m=0.20 kg and a=9.80m/s².

F= (0.20) kg x (9.80) 80m/s².

F=1.96kg m/s²

F=1.96 N, so acting force on an apple is 1.96N

Example 2:- A ball is falling out on the ground. Consider a ball weight 500g and gravity of the earth is 9.80m/s².What is the force acting on the ball due to the gravity?

F=ma

Here m=500g=500/1000kg=0.5kg and a=9.80m/s².

F= (0.5) kg x (9.80) 80m/s².

F=4.9kg m/s²

F=4.9 N, so acting force on a ball is 4.9N

Example 3:- A person pushing a block from one place to other place. If block weight is 10 kg and applied force is 20N, what is the acceleration of the block?

F=ma

a=F/m

Here m=10 kg and F=20 9.80m/s².

a= (20) N / (10) kg

a= (20) kg m/s² / (10) kg

a=2 m/s², so acceleration is 2 m/s².

       

10. Frequency:-Frequency is the number of cycle in unit time. Si unit of frequency is Hertz. Heinrich Rudolf Hertz (symbol Hz).

f=1/T=N/t

f=Frequency

T=Period

N=Number of cycles

T=Time amount

Example 1: - A valve open and close cycle takes 5 second. What is the frequency of this valve?

f=1/T

Here f=frequency, T=Period =5 seconds

f=1/5seconds

f=0.20 cycles/seconds

Generally cycles/second is known as hertz so frequency is 0.20Hz.

11. Ohm’s law:-

Ohm's law states that at a consistent temperature while all other physical parameters continue to be the same, the current flowing thru a conductor is at once proportional to the potential difference across its ends.

Ohms Law Formula,

V=IR

Here,
Voltage is V and is measured in Volts,

Example: If potential difference of 20 V is applied across a conductor and resistance is 30. Calculate the current flowing from it?

Answer:

Given: Potential difference V = 20 V,

Resistance R = 30 

V=I/R

V=20/30

V=0.6volts

12. Velocity:-

The velocity of an object is the change of its position with respect to the frame of reference, it is the function of time.

Velocity=Distance/Time

Example: - A motor cycle is covering 50Km distance in 1 hour, calculate the velocity of motor cycle.

Here Distance:-50km and time:-1 hours

So Velocity=Distance/time

                   =50Km/1 Hour

                   =50km/hour

13. Celsius to Fahrenheit calculation

F= (C X 1.8) +32

Example:-If the measured temperature showing on the display is 32° C, we need to read temp in Fahrenheit so convert the temperature unit.

Here measured temp=32° C

So F=32 X 1.8+32

        =89.6F

       

14. Fahrenheit to Celsius calculation.

 C= (F-32)/1.8

Example:-If the measured temperature showing on the display is 89.6F, we need to read temp in ° C so convert the temperature unit.

Here measured temp=89.6F

So C= (F-32)/1.8

        = (89.6-32)/1.8

        = (57.6)/1.8

        = 32° C

15.  Convert Celsius to kelvin by using equation.

K=Celsius+273.15

Example:-If the measured temperature showing on the display is 32° C, we need to read temp in Kelvin so convert the temperature unit.

Here measured temp=32° C

So K=Celsius+273.15

        =32+273.15

        =305.15 K

16. Convert kelvin to Celsius by using equation

Celsius=K-273.15

Example:-If the measured temperature showing on the display is 305.15 K, we need to read temp in Celsius so convert the temperature unit.

Here measured temp=305.15K

So Celsius=K-273.15

                 =305.15-273.15

                 =32° C

17. Convert hours into minutes

1 hour=60 minutes

Example:-If your device is measuring the time in hour but you want to show your data in minutes then you have to convert your data from hour to minutes. One machine is running for 3 hours so calculate the machine running minutes

Hear machine running time:-3 hours

                 So 1 hour =60 minutes

                 Here time is 3 hours

                 So running minutes=3 x 60=180 minutes

So calculate machine running time is 180 minutes

18. Convert hours in to seconds

1 hour=3600 seconds

Example:-If your device is measuring the time in hour but you want to show your data in seconds then you have to convert your data from hour to seconds. One machine is running for 1 hours so calculate the machine running seconds

Hear machine running time:-1 hour

                 So 1 hour =3600 seconds

                 Here time is 1 hour

                 So machine running seconds=1 x 3600=3600 seconds

19. Explain meter to centimeter conversion using example

1 meter=100cm

Example:-A person in the plant is measuring the length of the machine part and measured value is 10 meters as per his measuring device. But he needs measuring value in centimeters so convert 10meters into centimeters.

Here measured value is 10meters

So 1 meter =100cm

                  =10 x 100

                   = 1000 centimeters.

So measured value is 100 centimeters.

20. Explain centimeter to meter using example

1meter=100cm

Example:-A person in the plant is measuring the length of the machine part and measured value is 1000 centimeters as per his measuring device. But he needs measuring value in meter so convert 1000 centimeters into meter.

Here measured value is 1000 centimeters

So 1 meter =100cm

     ??          =1000cm

1000 cm X 1 meter/100 cm

                   =10 x 1 meter

                   =10meters

So measured value is 10 meters.

21. Explain kg to gram conversion with example

1 kg=1000 grams

Example:-A weighing scale is measuring weight of the material 10kg but operator needs to feed data in grams so convert the kg unit into gram unit by using formula.

Here weighing scale measured value is 10kg.

So 1kg =1000 grams

10 kg =??

=1000 grams X 10Kg/10Kg

=10000 grams

 So converted value is 10000 grams

22. Explain gram to kg conversion using example

1 kg=1000 grams

Example:-A weighing scale is measuring weight of the material 500 gram but operator needs to feed data in Kg so convert the gram unit into Kg unit by using formula.

Here weighing scale measured value is 0.5Kg.

So 1kg =1000 grams

500 grams =??

=500 grams X 1Kg/1000grams

=0.5 X 1kg

 So converted value for operator is 0.5 Kg

22. Explain triangle area equation using example

Area of triangle =1/2 X b X h

 Here, b=base and h=Vertical height

Example:-There is one triangle shape farm which height is 2m and measured base is 3m.What is the area of farm?

Here measured b=2m

And h=3m

So Area=1/2 x b x h

               =1/2 x 2m x 3m

               =6/2 m²

               =3m²

So farm are is 3m²

23. Explain square area equation using example

Area of square = a x a

 Here, a=length of the side

Example:-There is one square shape farm which both side length is 2m .What is the area of farm?

Here measured a=2m

So Area of farm=a x a

               = 2m x 2m

               =4 m²

               =4m²

So farm are is 4m²

23. Explain rectangle area equation using example

Area of rectangle = h x w

 Here, h=height and w=Width

Example:-There is one rectangle shaped ground which both height is 100 meters and width is 200 meters .What is the area of ground?

Here measured height=100 meters and w=200 meters

So Area of ground=h x w

               = 100m x 200m

               =20,000 m²

So ground area is 20,000m²

24. Explain area of parallelogram equation using example

Area of parallelogram = b x h

 Here, b=base and h=Vertical height

Example:-There is one parallelogram shaped ground which measured base is 10 meters and vertical height is 20 meters .What is the area parallelogram shaped ground?

Here measured b=10 meters and h=20 meters

So Area of parallelogram shaped ground=b x h

               = 10m x 20m

               =200m²

So ground area is 200m²

25. Explain area of circle using example

Area of circle

 Here, r=radius

Example:-There is one circle shaped ground which measured radius is 10 meters. What is the area circle shaped ground?

Here measured r=10 meters

So Area of circle shaped ground=

               = 3.14 x (10)²

               =3.14 x (100) m²

               =314m²

So circle shaped ground are is 314m²

26. Explain mass flow formula using example

Formula

 Here, Þ=Density of fluid

           V=Velocity of the liquid

            A=Area of cross section

Example:-Find the fluid mass flow rate whose density is 400kg/m³, velocity is 10m/s and cross section is 10cm²

So here,

Þ=400kg/m³

V=10m/s

A=10cm²=0.10m²

So

       = 400kg/m³ x 10m/s x 0.10m²=400Kg/s

27. Explain power formula using example

Formula

 Here, P=Power

           W=Work

            t=Time taken for work

Example:-Machine is doing work 200 J and taken time is 10s for that. So calculate the power used by machine

So here,

W=200J

t=5s

So

      W/t=200J/5s=40J/s=40watts

28. Explain work formula using example

Formula, Work=F x d

 Here, W=Work

           F=Applied force

            d=Displacement

Example: - A person is giving 10N force on a block and moving it 3m. Calculate the work done by person

 So here,

F=10N

d=3m

So W=F x d

          =10N x 3 m=30Nm

29. Explain resistance formula using example

Formula, R=V/I

 Here, R=Resistance

           V=voltage difference

            I=Current

Example: - Calculate the resistance of a wire having current flowing 2A and potential difference is 3 V

 So here,

I=2A

V=3V

So R=V/I

          =3/2

          =1.5 ohm

30. Explain velocity formula using example

Formula, V=s/t

 Here, V=Velocity

           s=Displacement

            t=time taken

Example: -A vehicle moves 100km distance in 1 hour. Calculate its velocity.

Here,

d=100km=100 x 10³m/s

t=1hour=1 x 3600 seconds

V=d/t=100km/1=100 x 10³ m/s/3600 s=28m/s

         

31. Explain gravity formula using example

Formula, F=Gm1m2/r²

 Here, G=Constant=6.67 x Nm²/kg²

           m1=Mass of the body 1

           m2=Mass of the body 2

             r =Radius or distance

Example: -Find the gravitational force if mass of object 1 is 2kg and mass of object 2 is 3kg.Consider distance 3cm

Here,                 

           M1=2kg

           m2=3kg

           r =3cm

So F=6.67 x 10-11 x 2 x 3/ (3 x 10-²)²

        =44,466 x

        =4.4 x N

      

32. Explain current formula using example

Formula, I=Q/t

Here, I=Current

          Q=Charge

           T=Time taken

Example:-In electrical panel, a lamp light for 1 hour and draws 0.6A current. Calculate the charge following trough lamp.

Here,

I=0.6A

t=1 hour=3600s

I=Q/t

Q=I x t =0.6A x 3600s=2160 C.

33. Explain π formula using example

Formula, π=Circumference/Diameter

Example:-A person measured 100cm around the outside of cylindrical shaped object. Calculate the diameter of the object.

Here,

Diameter= Circumference/π

               =100/3.14

               =31.84 cm