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Order of magnitude is a concept used to discuss the scale of numbers in relation to one another. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. [1] For example, 1 and 1.02 are within an order of magnitude.
An order-of-magnitude estimate is prepared when little or no design information is available for the project. It is called order of magnitude because that may be all that can be determined at an early stage. In other words, perhaps we can only determine that it is of a 10,000,000 magnitude as opposed to a 1,000,000 magnitude.
Objects with size order of magnitude 1e16m: Ten light-years (94.6 Pm) radius circle with yellow Vernal Point arrow; Bubble Nebula (NGC 7635), left; Dumbbell Nebula (NGC 6853), right; one light-year shell lower right with the smaller Cat's Eye Nebula (NGC_6543) and Barnard 68 adjacent. 1e16m lengths: Ten light-years (94.6 Pm) yellow shell ...
A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as an envelope. It is more than a guess but less than an accurate calculation or mathematical proof. The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
Thus one will expect to be within 1 ⁄ 8 to 8 times the correct value – within an order of magnitude, and much less than the worst case of erring by a factor of 2 9 = 512 (about 2.71 orders of magnitude). If one has a shorter chain or estimates more accurately, the overall estimate will be correspondingly better.
Chimpanzee probably not typing Hamlet. Mathematics – random selections: Approximately 10 −183,800 is a rough first estimate of the probability that a typing "monkey", or an English-illiterate typing robot, when placed in front of a typewriter, will type out William Shakespeare's play Hamlet as its first set of inputs, on the precondition it typed the needed number of characters. [1]
951 Gaspra, the first asteroid ever to be closely approached by a spacecraft (rough estimate) [125] 1 × 10 16 kg Rough estimate of the total carbon content of all organisms on Earth. [126] 3 × 10 16 kg Rough estimate of everything produced by the human species. [127] 3.8 × 10 16 kg Total carbon stored in the oceans. [128] 10 17: 1.6 × 10 17 kg
COCOMO consists of a hierarchy of three increasingly detailed and accurate forms. The first level, Basic COCOMO is good for quick, early, rough order of magnitude estimates of software costs, but its accuracy is limited due to its lack of factors to account for difference in project attributes (Cost Drivers).