Basically if we work backwards chronologically and look at the idea that Hercule was already retired from the Belgian police force when he arrived in England as a Belgian refugee in 1916, then by the time of his death in 1975 (some 60 years later) he is a staggering age.
The documents below suggest he was born in 1964, so by 1975 he would have been 111 years old.
This is a compilation based on 4 documents
based on the biography by Anne Hart
All cases are by Agatha Christie, unless stated otherwise.
"Cases in Commas" denote a short story, CASES IN CAPS denote novels
1864 Hercule Poirot and his twin brother Achille are born (Two points here:
1) There is some debate as to whether Achille is real or not, I am in favour of him being real;
2) A number of dates have been put forward for the birth of Poirot 1839 - 44, 1849- 54, 1864, 1884. Symons suggested 1864 which I took)
1864 The Holmes Family on their second continental tour visit the Poirots, who may be related through the Vernets (Suggested by the passage in THE LABOURS OF HERCULES where Poirot's friend Dr Burton is wondering how Poirot got his name "Thinking of an imaginary conversation. Your Mother and the Late Mrs Holmes, sitting sewing little garments or knitting: Achille, Hercule, Sherlock, Mycroft." Burton may have based this on a comment from Poirot)
Circa 1893 Poirot Joins either the French or Belgian Secret Service
1901 "Did Sherlock Holmes Meet Hercule-?" Short Story by Julian Symons in ELLERY QUEEN'S MYSTERY MAGAZINE Mid Dec 1987 Sherlock Holmes meets Poirot who is posing as the Chef of a French Diplomat.
1904 Hercule Poirot joins the Belgian Police and immediately becomes involved in the Abercrombie Case with Inspector Japp.
1909 "The Chocolate Box" ( in early version of this adventure Poirot makes reference to a younger sister Yvette, Poirot also refers to this case as taking place in 1893)
1914 Poirot has completed his mission in the Belgian police and is "due to retire" when Germany invades neutral Belgium. Poirot joins the resistance and is at one point saved by a French General.
1916 Poirot leaves Belgium and becomes a refugee in England.
July 1916 THE MYSTERIOUS AFFAIR AT STYLES
1918 "The Kidnapped Prime Minister"
"The Lemesurie Inheritance"1919 "The Affair at the Victory Ball"
1920 "The Disappearance of Mr Davisheim"
"The Plymouth Express"1921 "The Cornish Mystery"
"The Adventure of the Cheap Flat"
"The Submarine Plans"
"The Adventure of the Chapham Cook"
"The Tragedy at Marsden Manor"1922 "The Market Basing Mystery"
"The Mystery of Hunter's Lodge"
"The Adventure of the Egyptian Tomb"
"The Jewelry Robbery at the Grand Metropolitan"
"The King of Clubs"1923 "The Veiled Lady"
"The Adventure of the Italian Nobleman"
"The Double Clue" (Poirot meets Countess Vera Rossakoff for the first time.)
"The Adventure of Johnnie Waverly"
"The Case of the Missing Will"
"The Million Dollar Bond"
"The Adventure of the Western Star"
MURDER ON THE LINKS
"The Adventure of the Christmas Pudding" (This case was expanded and updated as "The Theft of a Royal Ruby" in the 1950's)1924 THE BIG FOUR (This adventure is the only appearance of Achille Poirot who dies at the end of this adventure. Countess Rossakoff aids Poirot, Poirot rescues the Countess' son Niki and is going to propose at the end of this adventure which has led to speculation that Poirot is Niki's father)
1925 Poirot is retired for a year
1926 MURDER OF ROGER ACKROYD
THE MURDER OF THE BLUE TRAIN1929 "The Third Floor Flat"
"The Underdog"1930 BLACK COFFEE (play by Christie)
"The Second Gong" (Expanded with new ending as "Dead Man's Mirror")
"The Mystery of the Baghdad Chest" (expanded and updated as "The Mystery of the Spanish Chest" in the fifties)1931 PERIL AT END HOUSE
1932 LORD EDGEWARE DIES
MURDER IN MESOPOTAMIASept "About Maigret and the Stolen Papers" by Julian Symons in THE GREAT DETECTIVES Maigret meet Poirot
MURDER ON THE ORIENT EXPRESS
1933 THREE ACT TRAGEDY (Poirot meets Mr Satterthwaite the associate of Harley Quin)
1934 Sept DEATH IN THE CLOUDS
1935 "How Does Your Garden Grow"
A CASE FOR THREE DETECTIVES by Leo Bruce (Poirot, Lord Peter Wimsey and Father Brown are all beaten to the solution of this case by Sgt William Beef.Jun - Nov THE ABC MURDERS
1936 June DUMB WITNESS
"Problem at Sea"1937 CARDS ON THE TABLE (Poirot meets Mrs Oliver, Superintendent Battle and Col. Race)
"Triangle at Rhodes'
"Murder in the Mews"
1938 Summer "The Adventure of the Orient Express" by August Derleth (Poirot meet Solar Pons, the Saint and Ashenden)
DEATH ON THE NILE (Col. Race)Dec HERCULE POIROT'S CHRISTMAS
APPOINTMENT WITH DEATH
1939 "Yellow Iris"
"The Dream"Jul SAD CYPRESS
ONE, TWO, BUCKLE MY SHOE
Late 1939 - Late 1940 THE LABOURS OF HERCULES
1941 Aug EVIL UNDER THE SUN
"Four and Twenty Black Birds"1942 FIVE LITTLE PIGS
1943 "Poirot and the Regatta Mystery" (Fellow Christie Investigator Parker Pyne earlier investigated a similar case called "The Regatta Mystery")
1945 Sept THE HOLLOW
1946 TAKEN AT THE FLOOD
1951 October MURDER IN PASTICHE by Marion Mainwaring (Poirot under the name of Atlas Poireau meets Trajan Beare (Nero Wolfe), Spike Bludgeon (Mike Hammer), Mallory King (Ellery Queen), Sir John Nappleby (Sir John Appleby), Jerry Pason (Perry Mason), Lord Simon Quinsey (Lord Peter Wimsey), Miss Fan Sliver (Maud Silver) Broderick Tournier (Roderick Alleyn))
1952 MRS MCGINTY'S DEAD (Mrs Oliver)
1953 AFTER THE FUNERAL
1954 HICKORY, DICKORY DOCK
1955 DEAD MAN'S FOLLY (Mrs Oliver)
1958 CAT AMONG THE PIGEONS
1962 THE CLOCKS (Poirot meets Colin Lamb the son of Superintendent Battle)
1963 THIRD GIRL (Mrs Oliver)
1968 HALLOWE'EN PARTY (Mrs Oliver)
1971 ELEPHANTS CAN REMEMBER (Mrs Oliver)
1972 MAFIA FIX by Richard Sapir and Warren Murphy (Poirot works with James Bond and Mr Moto and meets Remo Williams the Destroyer)
1973 THE STRANGE CASE OF THE END OF CIVILISATION AS WE KNOW IT (Poirot attends the Great Detective Conference held Arthur Sherlock Holmes as well as Columbo, Miles Messervy, Steve McGarrett, Sam Spade, Ironside and McCloud. The version seen of this was highly fictionalized as a spoof but it appears the Spade met his demise here and Poirot sustained injuries that caused him to be wheelchair bound for the rest of his life)
1974 CURTAIN (The Death of Poirot)
Has own practice in Europe, meets Inspector James Japp; later Captain Arthur Hastings
1916--Arrives to England as a Belgian refugee from WWI
Aided by Mrs. Inglethorpe of Styles Court, meets Hastings again
Solves murder at Styles Court with Hastings and Japp
Sets up practice in England, moves to 14 Farraway Street, London, with Hastings
1923--Poirot and Hastings solve murder in France, Hastings marries Dulcie and moves to Argentina
1925?--Poirot solves jewel theft, meets the Russian Countess Vera Rossakoff for first time
1926--Poirot unmasks member of the "Big Four" with Hastings, meets with Countess Rossakoff again
Retires and goes to King's Abbot to grow vegetable marrows for a year, solves the murder of Mr. Ackroyd
1928--While in France, Poirot solves a jewel theft and murder of American heiress, hires Georges as valet
1932--Poirot and Hastings (back from Argentina) are vacationing in St. Loo and uncover murder attempts
1934?--Poirot moves to 28 Whitehaven Mansions
1935--Poirot travels in airplane to England where a French moneylender is murdered, Japp helps
Poirot solves ABC Murders with Hastings (visits from Argentina) and Japp
1936--Poirot and fellow sleuths Colonel Race, Battle, and Ariadne Oliver solve murder of dinner host
1937--Poirot meets Colonel Race again and solves murder on the Nile River
Hastings helps Poirot solve case about "accident" of old lady
Poirot and Inspector Japp investigate a girl's suicide/murder
1939?--Felicity Lemon is hired by Poirot to be his secretary
1941--Poirot goes to the Jolly Roger Hotel and solves crime there
1946--Poirot unexpectedly sees Countess Rossakoff years later, now as a proprietor of a nightclub
1948--Poirot travels to Warmsley Vale to solve murder of young wife
1952--Poirot, Mrs. Oliver, Spence join to solve old lady's murder and clear an innocent man
1955--Miss Lemon's sister comes to Poirot asking for help at youth hostel
1956--Mrs. Oliver asks Poirot to help in a real murder hunt of a young girl
1963--Colin Lamb asks Poirot for help in murder of an unknown man
1969--Poirot joins forces with Spence (and Mrs. Oliver) in a Halloween Party murder
1972--Poirot helps Mrs. Oliver and Spence solve a decades-old murder/suicide
1975--Georges leaves employ of Poirot, Poirot goes to Styles Court
Poirot and Hastings track down murderer in Poirot's last case at Styles
Hercule Poirot, Belgian detective, dies at Styles Court