A running total or rolling total is the

summation In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, pol ...

of a sequence of numbers which is updated each time a new number is added to the sequence, by adding the value of the new number to the previous running total. Another term for it is

partial sum In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathemati ...

. The purposes of a running total are twofold. First, it allows the total to be stated at any point in time without having to sum the entire sequence each time. Second, it can save having to record the sequence itself, if the particular numbers are not individually important.

Method

Consider the

sequence In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is cal ...

(5, 8, 3, 2). What is the total of this sequence? Answer: 5 + 8 + 3 + 2 = 18. This is arrived at by simple summation of the sequence. Now we insert the number 6 at the end of the sequence to get (5, 8, 3, 2, 6). What is the total of that sequence? Answer: 5 + 8 + 3 + 2 + 6 = 24. This is arrived at by simple summation of the sequence. ''But'' if we regarded 18 as the running total, we need only add 6 to 18 to get 24. So, 18 was, and 24 now is, the running total. In fact, we would not even need to know the sequence at all, but simply add 6 to 18 to get the new running total; as each new number is added, we get a new running total. The same method will also work with subtraction, but in that case it is not strictly speaking a total (which implies summation) but a running difference; not to be confused with a

delta Delta commonly refers to: * Delta (letter) (Δ or δ), the fourth letter of the Greek alphabet * D (NATO phonetic alphabet: "Delta"), the fourth letter in the Latin alphabet * River delta, at a river mouth * Delta Air Lines, a major US carrier ...

. This is used, for example, when scoring the game of

darts Darts is a competitive sport in which two or more players bare-handedly throw small projectile point, sharp-pointed projectile, projectiles known as dart (missile), darts at a round shooting target, target known as a #Dartboard, dartboard. Point ...

. Similarly one can multiply instead of add to get the running product.

Use

While this concept is very simple, it is extremely common in everyday use. For example, most

cash register A cash register, sometimes called a till or automated money handling system, is a mechanical or electronic device for registering and calculating transactions at a point of sale. It is usually attached to a Cash register#Cash drawer, drawer fo ...

s display a running total of the purchases so far rung in. By the end of the transaction this will, of course, be the total of all the goods. Similarly, the machine may keep a running total of all transactions made, so that at any point in time the total can be checked against the amount in the till, even though the machine has no memory of past transactions. Typically many games of all kinds use running totals for scoring; the actual values of past events in the sequence are not important, only the current score, that is to say, the running total. The

central processing unit A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions ...

of computers for many years had a component called the accumulator. This accumulator, essentially, kept a running total; that is, it "accumulated" the results of individual calculations. This term is largely obsolete with more modern computers. A betting accumulator is the running product of the outcomes of several bets in sequence.

References

{{reflist , refs= {{cite book , title=Programmed Data Processor-1 Manual , date=1961 , publisher=

Digital Equipment Corporation Digital Equipment Corporation (DEC ), using the trademark Digital, was a major American company in the computer industry from the 1960s to the 1990s. The company was co-founded by Ken Olsen and Harlan Anderson in 1957. Olsen was president until ...

, location= Maynard, Massachusetts , url=http://bitsavers.trailing-edge.com/pdf/dec/pdp1/F15B_PDP1_Handbook_1961.pdf , url-status=live , archive-url=https://ghostarchive.org/archive/20221009/http://bitsavers.trailing-edge.com/pdf/dec/pdp1/F15B_PDP1_Handbook_1961.pdf , archive-date=2022-10-09 , access-date=2024-02-11

External links

cumulative at Wiktionary
a related term Operations on numbers

Method

Use

See also

References

External links