Whether you are wiring a project or sizing a component, a handful of electrical relationships do most of the work, and they all flow from one simple law. This guide explains them with practical examples, and ends with the safety basics that matter whenever real voltage is involved.
The three quantities: voltage, current and resistance
Three quantities describe any simple circuit. Voltage, measured in volts, is the electrical 'pressure' pushing charge around. Current, in amperes, is the rate of flow of that charge. Resistance, in ohms, is how much the circuit opposes the flow. A common analogy is water in a pipe: voltage is the pressure, current is the flow rate, and resistance is the narrowness of the pipe. Understanding these three intuitively makes every formula that follows feel natural.
Ohm's law: the foundation
Ohm's law links the three: voltage equals current times resistance, V = I × R. Rearranged, current is V ÷ R and resistance is V ÷ I. So a 12 V supply across a 6 ohm load drives a 2 A current. This one relationship, in its three forms, solves a huge share of practical electrical problems, which is why it is the first thing every electronics student learns. The Ohm's law calculator solves for whichever quantity you need.
Power in a circuit
Electrical power is voltage times current, P = V × I, in watts. Using Ohm's law it can also be written as I²R or V²÷R, whichever fits the values you have. Power matters because it becomes heat: components must be rated to dissipate the heat they generate, or they fail. The resistor power calculator shows the wattage a resistor must withstand, and the watts to amps calculator converts a device's power rating into the current it draws — useful for choosing cables and fuses.
Sizing a resistor for an LED
A classic beginner task is choosing the series resistor for an LED so it is not destroyed by too much current. You subtract the LED's forward voltage from the supply, then divide by the desired current: R = (Vsupply − Vled) ÷ I. For a 9 V supply, a 2 V LED and 20 mA, that is (9 − 2) ÷ 0.02 = 350 ohms. The LED resistor calculator does this and shows the power the resistor must handle.
Resistors in series and parallel
Resistors in series simply add up, increasing total resistance, and the same current flows through each. In parallel, the combined resistance is always less than the smallest resistor, because the current has more paths to flow, and each branch sees the full voltage. The series resistor calculator and parallel resistor calculator handle both, and the voltage divider calculator shows how two resistors in series split a voltage — the basis of countless sensor circuits.
Kirchhoff's laws
For circuits more complex than a single loop, two principles from Gustav Kirchhoff extend Ohm's law. The current law says that all the current flowing into a junction must flow out again — charge is not lost. The voltage law says that the voltages around any closed loop add up to zero — the energy supplied equals the energy used. Together with Ohm's law, these let you analyse almost any resistor network, and they underpin the series and parallel rules above.
AC, DC and mains basics
The examples here use direct current (DC), where current flows one way, as from a battery. Household mains is alternating current (AC), which reverses many times a second and is delivered at much higher, dangerous voltages. The same core ideas apply, but AC adds complications and real risk. Cables and fuses must be rated for the current they carry, which is why the watts-to-amps conversion matters when choosing them.
From theory to the workbench — safely
These calculations guide design, but on the bench, safety comes first. Always double-check ratings and never exceed a component's voltage, current or power limits, as exceeding them causes overheating, smoke or fire. Work on low-voltage, battery-powered circuits while learning, and treat mains electricity with the respect it demands. When in doubt — especially with house wiring — consult or hire a qualified electrician. The maths gives you confidence in a design; good habits and the right ratings keep you and your project safe while you build it.