Prince William counting down the start of a half-marathon this morning with George and Charlotte (Image: Ian Burt)

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Prince William spent Father's Day with his two oldest children at a half-marathon event.

Pictures emerged on Sunday afternoon showing the Duke of Cambridge, Prince George and Princess Charlotte gathering around a microphone and counting down to the start of the race around the Sandringham Estate.

George and Charlotte were photographed wearing shorts and trainers, while the duke was dressed in a blue shirt and a pair of navy chinos.

According to the event's website, Run Sandringham was welcoming hundreds of runners of all abilities and ages to run a half marathon, 5K or community mile, with the aim of raising "many thousands of pounds for good causes".

The website said: "With a start and finish within the royal estate, the event boasts a super scenic route around the grounds of Sandringham Estate, Her Majesty The Queen's winter retreat."

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The first-ever Run Sandringham saw hundreds of runners taking on three different routes
(Image: Ian Burt)

It is understood the duke was not running in the event and was there in a private capacity.

Shocked participants were seen getting selfies with the royal guests, who arrived to the surprise of everyone besides the organisers.

Meanwhile, the royal family Twitter account marked Father's Day by sharing a photograph from 70 years ago of the Queen with King George VI, the Duke of Edinburgh and the Prince of Wales.

The picture, captured at Balmoral in 1951, shows the Queen with her father and Philip at either side of her while Charles sits atop an animal statue.

All four are smiling in the black and white photograph, which was posted on the royal family Twitter feed.

The royal guests arrived to the shock of race participants, with some getting selfies
(Image: Ian Burt)

A message accompanying the image said: "To all dads everywhere, we wish you a very special Father's Day."

Clarence House posted pictures to mark the occasion including photographs of Charles with both his sons, William and the Duke of Sussex.

Another image shared by Clarence House featured Philip, while another showed the Duchess of Cornwall with her father Bruce Shand.

An accompanying message said: "To all papas everywhere, and to those who may be missing their dads today, we are thinking of you and wishing you a special £FathersDay."

The Cambridges also marked Father's Day by posting a notice board style video featuring pictures of William with his father and brother from their younger days and a wedding photo of Kate and her father Michael Middleton.

The post also included a previously unseen picture of William in uniform with his three children, and a photograph of the Queen and Duke of Edinburgh with their great-grandchildren.