An analog computer is a form of computer that uses electrical or mechanical phenomena to model the problem being solved, or more generally by using one kind of physical quantity to represent another. Modeling a real physical system in a computer is called simulation.

The similarity between linear mechanical components, such as springs and dashpots, and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics: They can be modeled using equations that are of essentially the same form.

However, the difference between these systems is what makes analog computing useful. If one considers a simple mass-spring system, constructing the physical system would require buying the springs and masses. This would be proceeded by attaching them to each other and an appropriate anchor, collecting test equipment with the appropriate input range, and finally, taking (somewhat difficult) measurements.

The electrical equivalent can be constructed with a few operational amplifiers (Op amps) and some passive linear components; all measurements can be taken directly with an oscilloscope. In the circuit, the (simulated) 'mass of the spring' can be changed by adjusting a potentiometer. The electrical system is an analogy to the physical system, hence the name, but it is less expensive to construct, safer, and easier to modify. The all-electronic analog computer is also extremely fast, since a calculation is completed at the rate at which a signal traverses the circuit, which is generally an appreciable fraction of the speed of light.

The drawback of the mechanical-electrical analogy is that electronics are limited by the range over which the variables may vary. This is called dynamic range. They are also limited by noise levels.

Other simulations can also be easily performed by these electric circuits. For example, water pressure can be simulated by voltage and water flow in terms of gallons per minute can be simulated by amperes.

There is a lack of understanding about electrical systems that sometimes leads to the terms analog and digital having seemingly confusing and somewhat dubious meanings. Analog systems are sometimes understood only as continuous, time variant electrical systems. From the above discussion this is not correct, since discontinuous functions may also be modeled. In fact, digital also has a precise technical definition. In the context of circuits, it refers to the use of discrete electrical voltage levels as codes for symbols and the manipulation of these symbols in the operation of the digital computer. The electronic analog computer manipulates the physical quantities of (waveforms) of volts or amperes. Consequently, the precision of the analog computer readout (of rational numbers) is limited only by the quantization of the readout equipment used (generally three or four places). The digital computer precision must necessarily be finite, but the precision of its result is limited only by time.

There is an intermediate device, a hybrid computer, in which a digital computer is combined with an analog computer. Hybrid computers are used to obtain a very accurate but imprecise 'seed' value, using an analog computer front-end, which is then fed into a digital computer iterative process to achieve the final desired degree of precision. With a three or four digit, highly accurate numerical seed, the total digital computation time necessary to reach the desired precision is dramatically reduced, since many fewer iterations are required. Or, for example, the analog computer might be used to solve a non-analytic differential equation problem for use at some stage of an overall computation (where precision is not very important). In any case, the hybrid computer is usually substantially faster than a digital computer, but can supply a far more precise computation than an analog computer. It is useful for real-time applications requiring such a combination (e.g., a high frequency phased-array radar or a weather system computation).

Some examples:

the abacus is a hand-operated digital computer (but not binary; it is biquinary)

the slide rule is a hand-operated analog computer

early gun directors used mechanical analog computers to direct gunnery fire