Ohm’s Law Tutorial: The One Formula That Runs Everything

Ohm’s law is the first formula in electronics and the one you will use in every single design decision. Voltage equals current times resistance. Master the triangle and the unit conversions, and most circuit questions answer themselves.
> At a glance: 7 minute guide · part of the electronics fundamentals complete guide track · worked example, quick-reference table and field notes included.

## The relationship and its triangle

V = I × R, rearranged as I = V ÷ R and R = V ÷ I. Draw the triangle with V on top. Cover the quantity you want and the arrangement of the other two shows the formula. It is geometry doing algebra for you.

## Units and realistic scales

Volts, amps, ohms — but real circuits talk in millivolts, milliamps and kilo-ohms. Convert before calculating: a 5 V rail feeding 4. 7 kΩ draws 1. 06 mA, not “1. 06 A” — the slipped prefix is the most common beginner arithmetic error.

## Power rides along

P = V × I combines with Ohm’s law into P = I²R and P = V²÷R. Every resistor choice is also a power decision. A 1 kΩ across 12 V dissipates 144 mW — fine for a quarter-watt part, marginal for an 0805 chip.

| Known values | Formula to use | Example |
| — | — | — |
| V and R | I = V ÷ R | 12 V ÷ 1 kΩ = 12 mA |
| V and I | R = V ÷ I | 5 V ÷ 20 mA = 250 Ω |
| I and R | V = I × R | 15 mA × 330 Ω = 4.95 V |
| Any two | P from the pair | P = I²R checks ratings |

## How to apply this in your build

Work through the sequence below. Each step assumes the previous one passed. The numbers that need arithmetic are covered by the linked tools at the end of this guide.
1. Convert all units to base before substituting
2. Solve for the unknown with the triangle
3. Compute power in every component the current passes through
4. Sanity-check: higher R means lower I at the same V

### Worked example

Sizing an LED resistor: (5 V − 2 V) ÷ 20 mA = 150 Ω. Power: 3 V × 20 mA = 60 mW — a standard quarter-watt resistor runs cool. The maths and the thermals agree. Cross-check with the Ohm’s Law Calculator and the result should agree to within rounding.

> Practical note from the bench. Every bench notebook we keep starts with the triangle drawn on page one — thirty years of engineers cannot all be wrong about a mnemonic.

## Who this guide is for

First-time readers get a single focused topic instead of a textbook chapter, with every term defined where it first appears. Returning readers use it as a reference. The table, the worked example and the mistake list answer the questions that come up mid-build. If you teach, the structure (theory, application, example, failure modes) maps cleanly onto a lab session.

## Prerequisites and preparation

Before starting: convert all units to base before substituting and solve for the unknown with the triangle. Keep the [Ohm’s Law Calculator](/tools/ohms-law) and [LED Resistor Calculator](/tools/led-resistor) open, every number in the worked example is reproducible. Total time including the bench steps: about 6 to 7 minutes.

## Common mistakes to avoid

Each of these has cost real hardware on someone’s bench, usually ours:
– Mixing milli and kilo prefixes mid-calculation
– Applying Ohm’s law to the whole circuit instead of the element in question
– Forgetting that resistance measurements need power off

## Key takeaways

– The relationship and its triangle — the foundation of this guide. Revisit it if any measurement here surprises you.
– Units and realistic scales — the foundation of this guide; revisit it if any measurement here surprises you.
– Power rides along — the foundation of this guide; revisit it if any measurement here surprises you.

### Quick reference card

| Aspect | Where to find it in this guide |
| — | — |
| Core theory | The relationship and its triangle |
| Application steps | How to apply this in your build |
| Worked numbers | Worked example |
| Failure modes | Common mistakes to avoid |

## How this fits the electronics fundamentals complete guide track

This guide is one stop in a structured path. Start from the [electronics fundamentals complete guide](/tutorial/electronics-fundamentals-complete-guide) pillar page for the full map, or continue with [voltage vs current](/tutorial/voltage-vs-current-explained) and [the passive trio](/tutorial/passive-components). For the arithmetic, open the [Ohm’s Law Calculator](/tools/ohms-law) or [LED Resistor Calculator](/tools/led-resistor).

## Frequently asked questions

When does Ohm’s law not apply?
Non-linear devices (diodes, LEDs) have no fixed R — apply the law to their linear companions instead.

Why do my measured and calculated values differ slightly?
Tolerance and temperature: a 5 % resistor at the edge plus heating explains most small gaps.

Is there a calculator for this?
Yes, the [Ohm’s Law Calculator](/tools/ohms-law) and [LED Resistor Calculator](/tools/led-resistor) run the formulas from this guide instantly, client-side, no signup.

## Continue the learning path

– The complete electronics fundamentals guide: [Electronics Fundamentals complete guide](/tutorial/electronics-fundamentals-complete-guide)
– Read next: [diodes and transistors explained: the two semiconductor families](/tutorial/diodes-and-transistors-explained)
– Also in this track: [passive components: resistors, capacitors and inductors compared](/tutorial/passive-components)
– Continue with: [the pn junction diode: physics, curves and applications](/tutorial/pn-junction-diode)
– Calculate as you go: [Ohm’s law calculator](/tools/ohms-law) · [resistor colour code decoder](/tools/resistor-color-code) · [RC time constant tool](/tools/rc-time-constant)
– Bookmark this page against the day a measurement surprises you. Most readers return to the table and the mistake list first, and that is the correct order.

## Measurement discipline

Keep a lab notebook entry for every build in this track. The measured values, the deviations from the guide and the reason for each. Six months from now, those notes are worth more than any tutorial. They describe your bench and your components rather than a general case.

When a result here disagrees with your expectation, write down both numbers before changing anything. The gap between predicted and measured is where the real engineering lives. It is usually a tolerance, a parasitic or an assumption that was never checked.
## Formulas and checks from this guide

Verification checklist for this track: measure before and after every change, confirm polarity before power-up. Log each value beside the guide’s stated number. If a reading differs by more than rounding, find out why before moving on, tolerance, wiring or an untested assumption is always the reason.

Bookmark this page against your next build in the track. The checklist above is the same one used across 29 guides in this series.

## Hard-won notes

Component tolerance and meter accuracy stack. A 5% resistor, a 2% reference and lead resistance easily explain small gaps. Compare direction and magnitude before suspecting the guide.

A resistor and capacitor kit, common diodes and transistors, a breadboard and jumpers. Add modules as tracks demand them.