[PYTHON] A formula that simply calculates the age from the date of birth

Formula and proof to simply calculate age from date of birth

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a formula

When you want to easily find the age from your birthday From today's date in yyyymmdd format, the birthday also in yyyymmdd format can be subtracted as is, and the integer part of the solution divided by 10,000 can be used as the current age.

For example, if today is August 18, 2017 and your birthday is August 20, 1990,

\begin{align}
\mbox{age}
&=floor\left(\frac{20170818-19900820}{10000}\right)\\
&=floor\left(\frac{269998}{10000}\right)\\
&=floor\left(26.9998\right)\\
&=26
\end{align}

$ Floor $ is the process of truncating the fractional part

The generalization of this is the following formula.

\begin{align}
\mbox{age}
&=floor\left(\frac{\left(\mbox{Current year}\times10000+\mbox{Current month}\times100+\mbox{Current date}\right)-\left(\mbox{Year of birth}\times10000+\mbox{Birth month}\times100+\mbox{birthday}\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }{10000}\right)
\end{align}

Calculation example

If today is 08/18/2017 and your birthday is 08/20/1990

\begin{align}
\text{age}
&= floor\left(\frac{\left(2017\times1000+08\times100+18\right)-\left(1990\times1000+08\times100+20\right)}{10000}\right)\\
&= floor\left(\frac{20170818-19900820}{10000}\right)\\
&= floor\left(\frac{269998}{10000}\right)\\
&= floor\left(26.9998\right)\\
&= 26
\end{align}

If today is 2017/08/20 and your birthday is 1990/08/20

\begin{align}
\text{age}
&= floor\left(\frac{\left(2017\times1000+08\times100+20\right)-\left(1990\times1000+08\times100+20\right)}{10000}\right)\\
&=floor\left(\frac{20170820-19900820}{10000}\right)\\
&=floor\left(\frac{270000}{10000}\right)\\
&=floor\left(27\right)\\
&=27
\end{align}

I just want to do something like "correct the elapsed milliseconds from UNIX time ..." with the spinal reflex, but when I think calmly, I think this logic is a very natural idea.

(For those who are not convinced [** Explanation here **](#% E6% 95% B0% E5% BC% 8F% E3% 81% AE% E3% 82% 84% E3% 82% 84% E8% A9% B3% E3% 81% 97% E3% 81% 84% E8% A7% A3% E8% AA% AC))

However, the definition of the age calculation formula may change depending on the target of use (especially in legal relations), so this calculation formula cannot always be used as it is.

code

When using JavaScript

`calcAge.js`


/**
 *A function that returns the age from the birthday
 * @param {!string} birthdayStr -Enter your birthday in yyyymmdd format
 * @return {number}Calculated age
 **/
var calcAge = function(birthdayStr){
  if(isNaN(birthdayStr)||birthdayStr.length !== 8){
    return -1;
  }
  var d = new Date();
  var dStr = ''+d.getFullYear()+('0'+(d.getMonth()+1)).slice(-2)+('0'+d.getDate()).slice(-2);
  return Math.floor((parseInt(dStr)-parseInt(birthdayStr))/10000);
};

console.log(calcAge('19900820'));

For Python 3.X

`calcAge.py`


# -*- coding: utf-8 -*-
from datetime import datetime
import math

def calcAge(birthdayStr):
  if not (birthdayStr.isdigit() and len(birthdayStr)==8):
    return -1
  dStr = datetime.now().strftime("%Y%m%d")
  return math.floor((int(dStr)-int(birthdayStr))/10000)

print(calcAge("19900817"))

The expression for return is

`python`


return (int(dStr)-int(birthdayStr))//10000

But OK.

In Ruby

`calcAge.rb`


require "date"
def calcAge(birthdayStr)
  if birthdayStr !~ /^[0-9]{8}$/
    return -1
  end
  return (Date.today.strftime("%Y%m%d").to_i - birthdayStr.to_i) / 10000
end

print calcAge("19900820")

In Ruby, the fractional part is arbitrarily truncated when dividing between integer types, so floor processing is not required.

In SQL

→ SQL date function (age calculation) | dbSheetClient IT technology blog

For PHP, Java, Perl

→ Yutaka Sano's server administrator diary --Simple formula to calculate age from date of birth: ITpro

In Excel

There is DATEDIF () function So this formula is unnecessary, but it is an effective means when the original data is not date type when importing and processing CSV.

=FLOOR.MATH((TEXT(TODAY(),"yyyymmdd")-[Date of birth in yyyymmdd format])/10000)

[FLOOR.MATH () Function](https://support.office.com/ja-jp/article/FLOOR-MATH-%E9%96%A2%E6%95%B0-c302b599-fbdb-4177-ba19- 2c2b1249a2f5) cannot be used in old Excel. In that case, use INT function OK if you use it.

=INT((TEXT(TODAY(),"yyyymmdd")-[Date of birth in yyyymmdd format])/10000)

Ilustration-The moment you get older

This formula calculates ** the current age **, but does not calculate ** how old you will be today **. [Age Calculation Niseki Suru Law](https://ja.wikipedia.org/wiki/%E5%B9%B4%E9%BD%A2%E8%A8%88%E7%AE%97%E3%83% According to 8B% E9% 96% A2% E3% 82% B9% E3% 83% AB% E6% B3% 95% E5% BE% 8B), ** the timing of aging ** is not the day of the birthday. ** The moment the day before the birthday expires ** (= 24:00: 0 the day before). That is, a person who was ** born on April 1, 2000 ** was 5 years old at the beginning of March 31, 2006, but will be 6 years old ** by the end of March 31, 2006, * * April 1, 2006 will be celebrated at the age of 6 **.

By this definition, even people born on February 29, leap year, age one year each year.

About birthday and grade

According to the School Education Law, ** people who are 6 years old by the day before April 1 ** are required to enter elementary school. "People born on April 1, 2000" are ** 6 years old on March 31, 2006, the day before April 1, 2006 **, so ** April 1, 2006 Became a first grader ** from the day. For the same reason, "people born on March 15, 2000" and "people born on April 20, 1999" are in the same grade.

"People born on April 2, 2000" have not reached the age of 6 the day before April 1, 2006, so they will be in the first grade of elementary school from April 1, 2007, the following year.

A slightly detailed explanation of mathematical formulas

For those who want to dig a little deeper. Even information on the year of birth and the current year can tell you how old you will be this year.

This year's age = current year-year of birth

However, I don't know "current age" because I don't know if I've reached this year's birthday. If ** is not celebrating this year's birthday **, then ** "current age" must be calculated ** by subtracting $ 1 $ from "this year's age".

This can be expressed by the ** case-specific formula ** as follows.

\begin{eqnarray}
\mbox{age}=\left\{
\begin{array}{ll}
\mbox{Current year}-\mbox{Year of birth}&\left(\mbox{Birth date}\leq\mbox{Current date}\right)\cdots\mbox{(1)Ceremony after this year's birthday}\\
\mbox{Current year}-\mbox{Year of birth}\color{red}{-1}&\left(\mbox{Birth date}>\mbox{Current date}\right)\cdots\mbox{(2)Ceremony until the day before this year's birthday}\\
\end{array}
\right.
\end{eqnarray}

By transforming the simple formula for age, a formula similar to the above ** case-specific formula ** can be created. The $ \ color {red} {red character part} $ of this transformed formula contains the process of "$ -1 $ if this year's birthday is not reached".

\begin{align}
\mbox{age}
&=floor\left(\frac{\left(\mbox{Current year}\times10000+\mbox{Current month}\times100+\mbox{Current date}\right)-\left(\mbox{Year of birth}\times10000+\mbox{Birth month}\times100+\mbox{birthday}\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }{10000}\right)\\
&=floor\left(\frac{\left(\mbox{Current year}-\mbox{Year of birth}\right)\times10000+\left(\mbox{Current month}-\mbox{Birth month}\right)\times100+\mbox{Current date}-\mbox{birthday}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }{10000} \right)\\
&=\color{red}{floor}\left(\mbox{Current year}-\mbox{Year of birth}\color{red}{+\frac{\mbox{Current month}-\mbox{Birth month}}{100}+\frac{\mbox{Current date}-\mbox{birthday}}{10000}}\right)\\
\end{align}

Replacing the ** total portion of the calculation results for the month and day ** of this formula with $ X $ results in a simple formula that is very similar to the ** case-specific formula ** that appeared earlier.

\begin{align}
\mbox{age}&=\color{red}{floor}\left(\mbox{Current year}-\mbox{Year of birth}\color{red}{+X}\right)\\\\
\color{red}{X}&=\frac{\mbox{Current month}-\mbox{Birth month}}{100}+\frac{\mbox{Current date}-\mbox{birthday}}{10000}\\\\\\
\end{align}

The range that the value of $ X $ can take is as follows

--When today is the day of your birthday

→ Current month = birth month, current date = birthday, so $ 0 $

--When today is December 31st and your birthday is January 1st

→ Maximum value $ X_ {max} $

\begin{align}
X_{max}&=\frac{\mbox{12}-\mbox{1}}{100}+\frac{\mbox{31}-\mbox{1}}{10000}=0.1130\\\\
\end{align}

--When today is January 1st and your birthday is December 31st

→ Minimum value $ X_ {min} $

\begin{align}
X_{min}&=\frac{\mbox{1}-\mbox{12}}{100}+\frac{\mbox{1}-\mbox{31}}{10000}=-0.1130
\end{align}

Therefore

-0.1130\leq X \leq 0.1130

Relationship between present and birthday within the year	XPossible value of
\mbox{Birth date}\leq\mbox{Current date}At (after birthday)	0\leq X_{after}\leq0.1130
\mbox{Birth date}>\mbox{Current date}At (before the day before the birthday)	-0.1130\leq X_{before}<0

Calculation after the day of this year's birthday

The result of "$ \ mbox {current year}-\ mbox {birth year} $" is always an integer greater than or equal to $ 0 $, which is $ 0 \ leq X_ {after} \ leq 0.1130 $. $ X $ does not affect the calculation result and is ignored.

\begin{align}
\mbox{age}
&=floor\left(\mbox{Current year}-\mbox{Year of birth}\color{red}{+X_{after}}\right)\\
&=\mbox{Current year}-\mbox{Year of birth}
\end{align}

This is consistent with the ** case-specific formula "(1) Formula after this year's birthday" **.

Calculation when the birthday of the year has not yet arrived

The result of "$ \ mbox {current year}-\ mbox {birth year} $" is always an integer greater than or equal to $ 0 $, which is $ -0.1130 \ leq X_ {before} <0 $. $ X $ has the effect of subtracting 1 from the calculation result for the year.

\begin{align}
\mbox{age}
&=floor\left(\mbox{Current year}-\mbox{Year of birth}\color{red}{+X_{before}}\right)\\
&=\mbox{Current year}-\mbox{Year of birth}\color{red}{-1}
\end{align}

This is consistent with the ** case-specific formula "(2) formula until the day before this year's birthday" **.

Therefore, the formula

\begin{align}
\mbox{age}
&=floor\left(\frac{\left(\mbox{Current year}\times10000+\mbox{Current month}\times100+\mbox{Current date}\right)-\left(\mbox{Year of birth}\times10000+\mbox{Birth month}\times100+\mbox{birthday}\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }{10000}\right)
\end{align}

The solution of is the same as the following formula, and the current age can be calculated from the birthday.

\begin{eqnarray}
\mbox{age}=\left\{
\begin{array}{ll}
\mbox{Current year}-\mbox{Year of birth}&\left(\mbox{Birth date}\leq\mbox{Current date}\right)\cdots\mbox{(1)Ceremony after this year's birthday}\\
\mbox{Current year}-\mbox{Year of birth}\color{red}{-1}&\left(\mbox{Birth date}>\mbox{Current date}\right)\cdots\mbox{(2)Ceremony until the day before this year's birthday}\\
\end{array}
\right.
\end{eqnarray}

Afterword

One of the interesting things about programming is how to make the processing in the brain ** concrete and put it into simple logic **. This code is simply packed with fun, so it was fun just looking at it.

If you are interested in Excel date processing, please also check here. → [Excel] Identity of date and time information --Qiita

For those who want to do more solid inspection of yyyymmdd format → Reading the regular expression that checks the validity of the date string in yyyymmdd format --Qiita

Reference link

-"Simple formula to calculate age from date of birth" is not always available --Nayami, a local government employee in charge of computerization -When do people get older after all: the best days for reading naname ―― Legal office column ―― Is the child born on April 1 born early? : House of Councilors Legal Affairs Bureau -About the grades of children born on April 1: Ministry of Education, Culture, Sports, Science and Technology -Age: Wikipedia