How is Gratuity of an employee calculated?

Is there a formula to calculate gratuity? 
Yes, there is one.
Indian laws suggest that an employee should be given gratuity for long term service. Gratuity is calculated by the formula,
G = (15/26)* N* (Monthly basic + Monthly DA)
where,
G - Gratuity
N - No of yrs of completed service (rounded)
DA - Dearness Allowance
15/26 - 26 stands here with the assumption there are 26 working days in a month while 15 stands for calculating 15 days of last drawn salary.

In a sense, one can assume the formula as Gratuity is 15 days of Basic + DA for every year of employment. Where, one day salary is calculated by dividing the monthly salary by 26days. If you find this statement confusing, stick to the above stated formula itself as they are all the same.

For an employee earning a basic + DA of Rs.20k per month and has worked more than 240 days for 7 continuous years,
Gratuity = (15/26)*7*20000

No. of years is calculated if an employee has completed more than 240 days in the respective years during service. If an employee has completed 7 years in a service but only in 6 years has attended more than 240 days then,
Gratuity = (15/26)*6*20000

N is the No. of years of service in which he/she has attended more than 240 days

Who is eligible for getting Gratuity paid?
The employee who have worked for at least a minimum of 5 years* in the organization is eligible for the gratuity when the term of employment ceases. Completion of continuous service of five years is not necessary where the termination of employment is due to death of disablement.

Maximum cap on Gratuity?
Yes, there is a limitation how much an employee can get gratuity. The maximum amount of Gratuity an employee can receive is Rs.3,50,000.

Employee gets different basic and DA during the term with an employer. Which amount gets counted for calculation purpose?
The last drawn 15 days salary. For example, you get your first year Basic and DA as Rs.8000/month and at the end of 7th year and during leaving the employment the Basic, DA combo is Rs.25000/month. Then Rs.25000 is the amount taken into consideration in the above formula.

Since the number of years is rounded, if an employee works with an organization for 4 years and 6 months does he/she become eligible for Gratuity?
NO.
After 5 years and up to 6 months should be counted as previous year and after 6 months to be counted as next year. Yes, rounding is allowed, but not for 4 years and 6 months. Rounding of months to years is allowed only after 5th year. However technically, if an employee has worked for minimum 4 years and 8 months with at least 240 days of no absence in the fifth year(the 8 months period) then the employee is eligible for gratuity.

Some examples below(years of service - no. of yrs for gratuity calculation):
5 years 2 months - 5 years
5 years 6 months - 6 years
4 years 7 months - Not Applicable
4 years 8 months** - 5 years
* Assumption that employee has worked at least for 240 days on all years of service.
** - Minimum period required for Gratuity applicability on satisfying the above assumption.

So effectively(with the assumption true), an employee who works for minimum 4 years and 8 months with an organization is eligible for gratuity as per Indian laws.

How to get Gratuity?
If gratuity is applicable, employee has to make an application in Form-I to his employer within 30 days from the date of gratuity becomes payable. Major organizations do get the required signature in this form on proper cease of employment with an employee.