- "Whoa. Is that an interdimensional extrapolator?"
"If that's nerd talk for 'breach device', then yes; and I need you to fix it."
- —David Chin and Laurel Lance[src]
An interdimensional extrapolator is a device created by Cisco Ramon that allows the user to open a breaches between different universes, or to allow instant travel between different locations within the same universe.
Jay Garrick has one of these instruments, presumably given to him by Cisco, which the former wears in a wristwatch-like fashion.
Josh also has one of these devices.
After the multiverse was destroyed and reborn, interdimensional extrapolators became unusable, even to open breaches between different points on the same Earth, as the rules of physics have dramatically changed.
Wishing to give Kara Danvers the ability to travel between Earths herself, Cisco Ramon created the interdimensional extrapolator and gave it to her as a gift, explaining that it had communication functionality between their dimensions. Kara later used it, opening a small breach from Earth-1 to Earth-38, traveling between them.
Sometime later, Winn Schott examined the device, being impressed by it. When the D.E.O. brought in a new prisoner, he hypnotized Kara, broke out of his handcuffs and took the interdimensional extrapolator, using it to transport himself to Earth-1.
J'onn J'onzz and Mon-El presumably made use of Kara's interdimensional extrapolator when they brought her to Earth-1 to get help from Team Flash as well as pursue Music Meister after he "whammied" Kara.
Kara and Alex used it to transport themselves to Earth-1 for Barry Allen and Iris West's wedding. After their trip, during which they helped to prevent a Earth-X invasion from an alternate universe, they used it to return to Earth-38.
Team Flash later enlisted Leo Snart's help to safely transport Neil Borman/Fallout into A.R.G.U.S. protective custody on Earth-1. Afterwards, Cisco gave Leo an interdimensional extrapolator of his own, suggesting that Leo and Ray, who were getting married, could use it to travel to Earth-1 for a honeymoon. Leo then used it to return to Earth-X.
When Team Flash was trying to come up with ideas of how to stop Cicada, Nora suggested that they enlist the help of another version of Harrison Wells. When Team Flash contacted Harrison Wolfgang Wells, he politely stated that he was too busy to help them, but instead recommended they turn to Harrison Sherloque Wells, regarding him to be the best detective in the multiverse, and gave Team Flash his coordinates. Since Cisco's hands had gotten cut in a fight against Cicada, thus making it painful to try to open a breach, Cisco used an interdimensional extrapolator to breach this new Wells to Earth-1. A short time later, in another confrontation with Cicada, who was hell-bent on killing Vibe, Cisco used Team Flash's interdimensional extrapolator to breach himself out of harm's way, as using his powers to open a breach was rendered impossible, not only due to his injured hands, but also because the presence of Cicada's dagger completely negated his powers.
After Nora was "whammied" by Spencer Young's phone, (she read a news article which hypnotized her into trying to kill Barry), Iris used an interdimensional extrapolator to breach herself to their location and knock Nora out with a tranquilizing dart.
Later, Barry was abducted by Rag Doll, who put power-dampening cuffs on the former and brought him to the top of a tall building, threatening to drop him. Since Cisco was still unable to open a breach due to his injuries, Iris contemplated using an interdimensional extrapolator to get herself to Barry's location to save him. However, this proved impossible since Sherloque had accidentally broken the team's only interdimensional extrapolator, and Cisco stated that it would take him at least an hour to fix the device.
Caitlin, Barry and Cisco used an interdimensional extrapolator to breach themselves to the north pole when they were searching for Caitlin's father, Thomas Snow. After they found him in an abandoned Tannhauser Industries black-ops site, the four of them then used the instrument to return to S.T.A.R. Labs. A short time later, Cisco used the extrapolator to return to the black-ops site where they'd found Thomas in order to investigate, as he suspected that Thomas was hiding something.
When Oliver and Barry each woke up one morning, and found that they'd swapped lives and realized that no one on Earth could tell who they really were, they decided to go to Earth-38 to find out if Kara would recognize Barry as Barry, and Oliver as Oliver, using Team Flash's interdimesional extrapolator to travel to her universe. A short time later, Querl Dox, Lois Lane and J'onn presumably made use of Kara's interdimensional extrapolator to travel to Earth-1 to aid Kara, Clark, Barry and Oliver in their battle against John Deegan.
When rounding up meta-human former criminals to transport them into protective custody in an effort to keep them safe from Orlin Dwyer; a serial killer known as Cicada, who'd begun targeting meta-humans with known criminal pasts, Barry (as The Flash) approached Shawna Baez, a meta-human also known as Peek-a-boo (whom Team Flash had fought before), at a bar, asking her to come with him for her own safety. When Cicada showed up, Barry left Shawna with an interdimensional extraplator, telling her to use it get out of there. Barry then engaged in a fight with Cicada, seeking vengeance after Orlin had severely injured Nora; Barry's daughter from the future. However, he ended up having to retreat and go with Peek-a-boo, as she was having trouble figuring out how to work the device.
It's possible that Laurel Lance of Earth-2 has one of these devices, since, after officially leaving her criminal past behind her, she decided to go back to her home universe and operate there as a symbol of hope to the people of Earth-2 by formally taking up the mantle of the Black Canary. She later traveled back to Earth-1 to aid Team Arrow in their battle against the Ninth Circle, and subsequently returned to Earth-2 at some point afterwards.
When the Monitor sent Oliver to Earth-2 as part of their mission to prepare for the impending Crisis, John borrowed an interdimensional extrapolator from Cisco to travel to Earth-2 to help Oliver out. When Earth-2 ended up getting swallowed by a mysterious energy wave, John and Oliver, accompanied by Earth-2 Laurel, used the instrument to escape the destruction by fleeing to Earth-1. Shortly after this, at her first available opportunity, Laurel wished to go back to Earth-2, refusing to believe that her entire home universe had simply vanished. Since the device had seemingly been damaged in their escape from Earth-2, Laurel tracked down David Chin (an associate she knew from her time working with Cayden James) and had him fix it. After this, she attempted, once again, to return to her universe. However, as she learned that while device was working just fine and could still take her to other universes, no signal existed on Earth-2, forcing her to face the fact that her world was destroyed.
When Barry tried to run into the future, to December 11, 2019 to see what happened after he, according to the Monitor, died in the Crisis on December 10, 2019, Barry found his path through the Speed Force blocked by antimatter. This ended up giving him an injury that left him in a considerable amount of pain, prompting him to go to Earth-3 to get help from Jay Garrick; an expert on antimatter. While there, he met Jay's wife, Joan Williams (Barry's mother's Earth-3 counterpart), who was also a fellow scientist of Jay's. The two of them informed Barry that while it may not be possible for them to physically send him into the future, they may be able to project his mind into the future to see what was to come. This ended up leaving Barry worn out and in a good deal of greater agony, and they subsequently brought him back to Earth-1 to rest, as Barry insisted on seeing Iris. Later, they returned to Earth-3 using an interdimensional extrapolator in Jay's possession, potentially given to him by Cisco.
While searching for the Paragons, Kate Kane and Kara used an interdimensional extrapolator to go to Earth-99, as Mar Novu had told them that going there would lead them to the Paragon of Courage (whom they later learned was Kate herself).
Cisco Ramon later revealed that he still contains the former method of time travelling, thanks to the pre-Flashpoint version of himself.
DC's Legends of Tomorrow