Rel
A rel was a Dalek unit of measurement, principally of time.
Definition
One account specified that a rel was slightly longer than a second but shorter than a second and a half. (PROSE: Buyer's Remorse) Another account, the reconnaissance scout's countdown, implied rels to be longer, however. Indeed, the Thirteenth Doctor displayed confusion as to exactly how long a rel was. (TV: Resolution)
The Daleks used rels for time measurement, (AUDIO: The Genocide Machine, The Mutant Phase, The Four Doctors, Blood of the Daleks, TV: Doomsday, COMIC: The Dalek Project) having inherited it from the Kaleds before them. (AUDIO: Guilt, The Master's Dalek Plan) The Unbound Master described rels as a "non-decimal time unit". (AUDIO: Shockwave)
When the New Dalek Empire tried to destroy the omniverse with a reality bomb powered by an arrangement of planets in the Medusa Cascade, they launched a countdown from two hundred rels until they would attempt to use it. (TV: Journey's End)
In other contexts, it was a unit of speed. (COMIC: Plague of Death, The Emissaries of Jevo)
In yet another account, it was used to measure hydro-electricity. (PROSE: The Dalek Dictionary)
Usage
Within the sphere chamber of Torchwood Tower in 2007, Dalek Jast ordered that the communications barrier be rewinded by nine rels, having spotted the image of the Tenth Doctor during the contact with Cyber-Leader One. (TV: Doomsday)
In 1930, Dalek Caan, after reporting in minutes, called out a countdown of forty rels before a gamma strike hit the Empire State Building. (TV: Evolution of the Daleks)
Aboard the Crucible, a Dalek called out a countdown of ten rels before the Doctor's TARDIS was seemingly destroyed by the Z-Neutrino core. Later, the Supreme Dalek called a countdown of ten rels prior to testing the calibration of the reality bomb. Once the planetary alignment field was activated, the Supreme Dalek began a countdown of two hundred rels to universal reality detonation. Finally, the Supreme Dalek called down the last twenty rels only for the bomb to be stopped at the last moment by the DoctorDonna. (TV: Journey's End)
Aboard a Dalek flying saucer in 1941, the first Strategist Dalek of the New Dalek Paradigm reported that a time jump would be performed in thirty rels. (TV: Victory of the Daleks)
The Twelfth Doctor found that one corner of the galaxy had adopted the Dalek time measurement of rels after a series of wars and other struggles. (PROSE: Buyer's Remorse)
When the Reconnaissance Dalek predicted conquest of Earth in 9376 rels, the Thirteenth Doctor had trouble remembering how long a rel was. (TV: Resolution)
During a time loop in the last few minutes of New Year's Eve 2020, a newly-arrived Dalek Executioner informed Dan Lewis that it had arrived "1.93 rels ago". (TV: Eve of the Daleks)
Other uses
A Rel counter was in use within Professor Zaroff's laboratory. (TV: The Underwater Menace)
"Rel" was also used in an idiomatic sense. When Rose Tyler revealed she had been on a Lect ship, Glom said, "Wait a rel," before declaring she was with the "Riders". (COMIC: Weapons of Past Destruction)
Behind the scenes
Before appearing in early Doctor Who comics, the word rel originated in one of the non-narrative pieces of fiction in The Dalek Book, namely The Dalek Dictionary. There, they were defined as a unit of measurement of hydro-electricity, not time. The film Daleks' Invasion Earth 2150 A.D., meanwhile, was the first source to use the term as a Dalek measurement of time, prominently displaying a countdown in rels.
Given that the 50 rels on the counter in Daleks' Invasion Earth 2150 A.D. are arranged similar to a typical clock, it is generally said by fans that rels are equal to 1.2 seconds. If this was true, then the 9376 rels mentioned in TV: Resolution would be approximately equivalent to 3 hours, 7 minutes and 31 seconds.
However, Terry Nation Army Episode 4 points out that the timer prop existed prior to Doctor Who by at least three years - appearing in shows as early as 1960 and even making a brief appearance during an episode of The Underwater Menace (with the Rel label still attached). Another prop of the same design also appeared in The War Machines. Thus, the prop was not designed to make any specific intention as to the length of a rel.
It is not unheard of for units in physics to be denoted by the same dimension even though in "standard" systems of measurement they're considered to refer to different dimensions. For example, mass, momentum, and energy in natural units. This is generally accomplished by defining certain physical constants as being fixed and dimensionless, such as Planck's constant and the Speed of light. However, natural units treat velocity as dimensionless (per treating the speed of light as dimensionless), and have energy and time as inverses of the other (per treating Planck's constant as dimensionless), so if this is how the Daleks interpret Rels, neither of these physical constants will be dimensionless in their scheme.
