So, How is the Age of the Earth and Universe Calculated?

The age of the Earth has been contemplated by man for centuries. One of the first making a serious attempt at calculating its age was Bishop James Ussher, who at age thirteen entered Trinity College Dublin. He was born in 1581 and ordained a priest in 1601 rising to professor at Trinity by 1607. Then in 1625 he was appointed Archbishop of Armagh heading the Anglo-Irish church.
WWWHis method of calculation was the use of the Hebrew Bible genealogy, and an in-depth study of  Greek, Roman and Chaldean history which represented all of known European history at the time. His conclusion? The first day of creation occurred on Sunday, October 23, 4004 BC, therefore, Earth was 6000 years old. From what I could understand, his calculation was the beginning of everything—man, the Earth and the universe—since there were no eye-witness accounts for the period preceding man, he assumed the literal interpretation of Genesis. He was not alone. He was supported by the great Sir Isaac Newton, astronomer Johannes Kepler, scholars Venerable Bede and Scaligar; all coming to similar calculations.
WWWIn 1862, the British mathematical physicist Lord Kelvin, widely known for determining the correct value of absolute zero at approximately –523.670 F, made the first calculation of the Earth’s age without the Bible. He knew that Earth’s temperature increased one degree Fahrenheit for each fifty feet you go into the ground, and guessed that Earth began as molten rock at 7,0000 F, then calculated how long it would’ve taken to cool. After refining his initial estimate of 400 million years, he calculated Earth at 24 million years old.
WWWThen along came Ernest Rutherford, known as the father of nuclear physics. In 1904 he presented a paper at the Royal Institute in London, announcing the Earth was 700 million years old, and Kelvin was in the audience sleeping through most of Rutherford’s presentation. His discovery of radioactive decay was the foundation of his calculation.
WWWRadioactive decay is the breakdown of unstable atoms into smaller stable ones. For instance, unstable uranium breaks down into stable lead, and the rate occurs at a fixed speed, always. So, by looking at the proportion of uranium to lead within the rock, you can determine how long it took to change into that proportion, and Earth’s crust is rich with radioactive unstable elements. This decay allows a direct measurement of rocks, called geochronology or radiometric dating. Rocks are atomic clocks. The race was afoot to find the oldest rocks.
WWWThe problem is that rocks become eroded due to exposure to weather, making it exceedingly difficult to find old rocks. But there are pristine rocks available—they come from space, rocks that were formed the same time the Earth and our solar system were formed—asteroids. And fortunately they fall into our laps as meteorites. Almost all meteorites have the same radiometric age…4.5 billion years old, as is the Earth and our solar system. Rutherford expanded geological time by a factor of 100.
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OLDEST ROCK

On February 8, 1969, a stone approximately the size of a car, and traveling at ten miles per second, exploded over Allende, Mexico, breaking up into thousands of fusion encrusted pieces. The Allende stones became one of the most widely distributed meteorites, providing scientists a wealth of material to study. They are the oldest known matter at 4.567 billion years old, 30 million years older than Earth, and 287 million years older than the oldest rock known on Earth.
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THE UNIVERSE
We live in an ever expanding universe. The vast majority of galaxies are moving away from each other and they’re all moving at different speeds depending how far away they are. The galaxies further away are moving faster than those that are closer. In other words, not only is the universe expanding, it’s doing so at an accelerated pace.
WWWA great analogy I’ve come across is to consider a loaf of raisin bread, the raisins representing galaxies, and the dough being the fabric of space. As the dough rises, it carries the raisins with it, pulling them apart from each other, the raisins on opposite sides of the loaf will move further from each other than the raisins that were nearer each other. Stated simply, the speed of their motion is proportional to the separation between them.
WWWAstronomers determine a galaxy’s motion by observing its light spectrum, galaxies moving away make it appear redder, called the red shift, and used to calculate the velocity of many galaxies and then plotted. This is called the Hubble constant or the rate of expansion. Then it’s a matter of dividing the distance by the velocity to give them the time, or age. It’s like playing time backwards. WWWAnother technique is the measurement of Cosmic Microwave Background (CMB) from the faint glow left by the Big Bang—the radiation that streamed into space when the universe was 300,000 years-old,  showing up as hot and cold spots on temperature maps. The older the universe, the farther these spots lie from Earth, and the smaller they appear on the sky. From the size of the spots, scientists can calculate the age of the universe.
WWWFrom these methods of measurement astronomers have precisely calculated the age of the universe to be 13.75± 0.13 billion years-old.