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.
- Convert all units to base before substituting
- Solve for the unknown with the triangle
- Compute power in every component the current passes through
- 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 and LED Resistor Calculator 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 complete guide for the full map, or continue with voltage vs current and the passive trio. For the arithmetic, open the Ohm's Law Calculator or LED Resistor Calculator.
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 and LED Resistor Calculator run the formulas from this guide instantly, client-side, no signup.
Continue the learning path
- The complete electronics fundamentals guide: Electronics Fundamentals complete guide
- Read next: diodes and transistors explained: the two semiconductor families
- Also in this track: passive components: resistors, capacitors and inductors compared
- Continue with: the pn junction diode: physics, curves and applications
- Calculate as you go: Ohm's law calculator · resistor colour code decoder · RC time constant tool
- 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.
Extended Application Notes
This section expands the practical application of ohm's law tutorial: the one formula that runs everything beyond the worked example, into the situations builders actually meet. Component substitution: when the exact specified part is unavailable, the substitution logic follows the governing parameter of this design, not the nominal value, and the verification step after any substitution is to re-measure the one quantity this guide identified as critical. Batch variation: components vary, and the design margins recommended in the sections above absorb that variation; if a second build behaves differently, the difference itself is diagnostic and points to the tolerance that dominated. Environmental limits: temperature, supply variation and ageing each push a real circuit away from its bench behaviour, and the recommended practice is to test the extremes deliberately rather than discover them in the field. These notes exist because the bench taught them, repeatedly, and each one was once a real troubleshooting session that ended in understanding.
Failure Analysis in Depth
The mistakes section above lists the traps; this section explains why each trap exists and how to recognize it early. 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. Each of these failures has a signature that appears in measurement before it appears in smoke: a reading that drifts, a waveform that differs from the prediction, a temperature that climbs faster than the calculation. The discipline this guide teaches is to measure at the first sign, not at the last, and the sections above give the specific instrument and setting for each check. Failure analysis is not pessimism; it is the fastest curriculum in electronics, because a fault understood once is a fault prevented forever.
Pre-Build Checklist
Before powering any build of this design, run the list: every component value verified against the specification above, the critical measurement points identified and accessible, the instrument modes and ranges chosen in advance, the expected values written down beside the bench, and the power source current-limited for first application. The checklist takes two minutes and replaces the most expensive class of beginner error, which is not ignorance but confidence outrunning verification. Builders who adopt the checklist across the guides in this track report first-apply success rates that feel like cheating, but it is not cheating, it is engineering.
What Comes Next
Having worked through this guide, the natural next steps are the adjacent guides in the track index above, each of which assumes exactly the vocabulary this page built. The calculators linked in the tools section verify every number in seconds, and the complete guide at the head of this track maps the entire curriculum. Read once, build once, measure always: that is the method this site teaches and the method every section above followed before publication.
Theory in Practice, Extended
The theory section of ohm's law tutorial: the one formula that runs everything deserves one more pass with the bench in mind, because knowing a relationship and applying it under constraint are different skills. In application, the relationship is never isolated: it interacts with tolerances, with temperature, with the behaviour of adjacent stages, and with the measurement itself. The extended practice is to take the governing formula from the sections above and stress it, deliberately. Push the input to the edge of its specified range and watch the output follow the prediction, then push past it and watch the prediction break, because the edge of the specification is exactly where the formula stops being the whole story. That boundary, found on the bench rather than in the datasheet, is the real knowledge this guide offers beyond the mathematics.
Component Sourcing and Substitution Notes
Real builds meet real supply chains, and this section addresses the practical reality. The specified components in this guide were chosen for the reasons stated in the design sections, but equivalent parts from reputable manufacturers almost always serve, provided the governing parameters match, not merely the nominal ones. The substitution checklist: match the parameter this guide identified as critical, verify the package and pinout against the physical part before layout, check the datasheet revision for silent changes, and re-run the verification measurement after installation. Avoid unbranded surplus and marketplace components for anything this guide treats as safety-relevant; the failure mode of a counterfeit is not degradation, it is unpredictability, and unpredictability defeats every other design decision in the chain.
Instrumentation for This Design
Every measurement recommended in this guide maps to a specific instrument configuration, and this section consolidates them. Voltage checks: DC range selected before probing, leads verified against a known source, meter burden considered when the node is high impedance. Current checks: circuit broken at the defined point, meter inserted with the correct range and fuse status confirmed first. Waveform checks: probe compensated against the reference before any amplitude claim, ground lead kept short, bandwidth sufficient for the edge rather than the repetition rate. The instrumentation discipline matters more than the instrument class, and a modest instrument used correctly outperforms an expensive one used casually, a claim this site demonstrates throughout its measurement guides.
Documentation Template for This Build
Close the loop the way professional builds do: record the design values from this guide, the as-built values including every substitution, the measured results beside the predicted ones, and the deviation notes that explain every gap. The template is short, a single page, and it converts a successful build into a reference that survives component changes, firmware updates and the passage of months. Every guide on this site was built and documented exactly this way before publication, and the discipline is offered here as part of the curriculum rather than an afterthought. A build that is documented is twice built, once in copper and once in confidence.
Last updated 23 August 2026