Ohm's Law

Ohm's law is the rule that ties together the three most basic quantities in electronics: voltage, current and resistance. It fits in three letters, V = I × R, and it answers questions like "how much current will flow?" or "what resistor do I need?" This page explains each quantity from the start, shows the three ways to write the law, and gives you a live calculator to try your own numbers.

1. Voltage, current and resistance

Everything around you is made of atoms, and atoms contain tiny particles called electrons that carry a negative electric charge. In a metal wire, some electrons are loosely held and can drift from atom to atom. Article 1, What is Electronics, explains where these free electrons come from. Three ideas describe what they do:

• Current is the rate at which charge flows past a point: how much charge goes by each second.^[1] More charge per second means more current. Its letter in equations is I.
• Voltage (properly, potential difference) is the energy each bit of charge gains or loses as it moves between two points.^[2] A battery gives charge energy; a resistor takes it away as heat. Voltage is always measured between two points, never at one point alone. Its letter is V.
• Resistance is how strongly something opposes the flow of current. In a metal, the drifting electrons keep colliding with the vibrating atoms, and every collision turns some of their energy into heat.^[1] Its letter is R. A part made to have a definite, stable resistance is called a resistor; Article 3, Resistors, covers them in detail.

For any current to flow, the charge needs a complete loop to travel around, from the battery's one terminal, through the parts and back to its other terminal. That loop is a circuit.^[3] If the loop is broken anywhere, the current stops everywhere in it.

Why "I" for current? It is usually said to stand for the "intensity" of the flow, though even textbook authors note that the origin is disputed. Some older books also write E (for electromotive force) instead of V.^[4] You will meet both.

2. Units and symbols

Each quantity has its own unit in the International System of Units (SI, the modern metric system), and each unit is named after a scientist.^[5]​^[4]

A coulomb (C) is the SI unit of charge; one coulomb is the charge of about 6.24 × 10¹⁸ electrons, so one ampere means that many electrons passing each second.^[6] A joule (J) is the SI unit of energy. So 1 V = 1 J/C,^[2] 1 A = 1 C/s,^[1] and 1 Ω = 1 V/A.^[3] NIST, the U.S. standards agency, lists the volt and the ohm as SI units with special names and notes that electric potential difference is also called "voltage" in the United States.^[5]

The ohm's symbol, Ω, is the capital Greek letter omega.^[3] Where it is hard to type, people write "ohm" or "R" instead (a part marked 4R7 is 4.7 Ω; Article 3 explains these markings).

Prefixes: k, M, m and µ

Real values span a huge range, so units take a prefix, a letter in front that multiplies them by a power of ten.^[5] Only a few matter here:

Note the capital and small letters: M (mega) and m (milli) differ by a factor of a billion.^[5] When you calculate, convert to plain volts, amperes and ohms first, or use the shortcut in section 4.

3. The law itself

In 1827 the German physicist Georg Simon Ohm published his finding that the current through a metal wire is directly proportional to the voltage across it, at a given temperature.^[4]​^[3] "Directly proportional" means that if you double one, the other doubles too: twice the voltage pushes twice the current through the same wire. Written as an equation:

I = V ÷ R, or, rearranged, V = I × R

The resistance R is the fixed number that links the two. A large R means only a little current flows for each volt; a small R lets a lot flow.^[3] OpenStax describes this as cause and effect: the voltage is the cause, the current is the effect, and the resistance sets how big the effect is.^[3]

Figure 1 also shows how each quantity is measured. An ammeter measures current and must be placed in the path of the current, because parts in series carry the same current. A voltmeter measures voltage and is connected across the part, because parts in parallel share the same voltage.^[7] A multimeter, the hobbyist's standard meter, does both (and measures resistance), depending on how you set it and where you plug the leads. Article 9, DC Circuits, shows how to use one.

The voltage across a resistor is often called its voltage drop or "IR drop," because it equals I × R. Measured around a circuit, voltage rises at the battery and falls at the resistor.^[3]

4. Three ways to write it

Ohm's law is one equation, but you can solve it for whichever quantity you do not know. Here is the algebra, step by step, starting from V = I × R:

1. To find voltage, use it as is: V = I × R.
2. To find current, divide both sides by R. On the right, R ÷ R cancels to 1, leaving I = V ÷ R.
3. To find resistance, divide both sides of V = I × R by I instead, leaving R = V ÷ I.^[3]

If algebra is rusty, the triangle in Figure 2 is a memory aid: cover the letter you want, and what is left shows the formula.

A shortcut for common units

Hobby circuits mostly use volts, milliamperes and kilohms, and those three fit together neatly because the "milli" (1/1,000) and "kilo" (1,000) cancel (calculated from the prefix values above):

• volts ÷ kilohms = milliamperes (5 V ÷ 10 kΩ = 0.5 mA)
• milliamperes × kilohms = volts (2 mA × 4.7 kΩ = 9.4 V)
• volts ÷ milliamperes = kilohms (3 V ÷ 10 mA = 0.3 kΩ = 300 Ω)

Mixing other units without converting (volts ÷ ohms when the current is in milliamperes, say) is a common beginner mistake, and it makes answers wrong by a factor of 1,000.

5. The calculator

Type values into any two boxes and the third is calculated for you, along with the power in the resistor (section 7). The line under the boxes shows which form of the law was used, with your numbers filled in. A few details:

• Which box is calculated? The highlighted one, marked "Calculated." Use the Solve for buttons to choose it, or simply type in it: the box you used least recently then becomes the calculated one.
• Units. Pick mV, mA, kΩ and so on from the list beside each box instead of typing letters. The calculated box picks a sensible unit by itself; change it if you prefer another.
• Checks. Resistance must be more than zero, values cannot be negative, and boxes must hold plain numbers. If something is off, a message explains it instead of showing a nonsense answer.
• The drawing is the circuit from Figure 1. Its labels follow your numbers, and the resistor turns orange when it would make more heat than a common ¼ W resistor can handle.

The calculator assumes an ideal resistor: one whose resistance stays the same whatever the voltage. Section 8 explains when that is not true.

6. Worked examples

Each example follows the same three steps: write down what you know in plain units, pick the form of the law that gives the unknown, then calculate. All results here are calculated.

Example 1: 9 V across 220 Ω (find the current)

Known: V = 9 V, R = 220 Ω. Unknown: I, so use I = V ÷ R.

I = 9 V ÷ 220 Ω = 0.0409 A = 40.9 mA

The power in the resistor is P = V × I = 9 V × 0.0409 A ≈ 0.37 W. That is more than a common ¼ W (0.25 W) resistor is rated for, so it would overheat. A ½ W part would be just inside its rating; the twice-the-power habit from section 7 points to a 1 W part.

Example 2: 5 V across 10 kΩ (find the current)

Known: V = 5 V, R = 10 kΩ = 10,000 Ω. Use I = V ÷ R.

I = 5 V ÷ 10,000 Ω = 0.0005 A = 0.5 mA = 500 µA

With the shortcut from section 4: 5 V ÷ 10 kΩ = 0.5 mA, the same answer. The power is 5 V × 0.0005 A = 0.0025 W, or 2.5 mW: tiny. Resistors of 10 kΩ often connect a microcontroller's input pin to 5 V (a "pull-up"), exactly because so little current and heat result.

Example 3: 12 V and 2 A (find the resistance)

Known: V = 12 V, I = 2 A. Unknown: R, so use R = V ÷ I.

R = 12 V ÷ 2 A = 6 Ω

The power is 12 V × 2 A = 24 W. A load like this is usually a heater, motor or lamp, not a small resistor; a resistor doing this job would be a large power resistor, often mounted on a heat sink.

Example 4: 20 mA through 330 Ω (find the voltage)

Known: I = 20 mA = 0.020 A, R = 330 Ω. Use V = I × R.

V = 0.020 A × 330 Ω = 6.6 V

So 6.6 V would appear across the resistor. Checking it the other way: 6.6 V ÷ 330 Ω = 0.020 A. Running a result backward through another form of the law is a quick way to catch mistakes.

Example 5: choosing an LED resistor

An LED (light-emitting diode) must have its current limited, usually by a resistor in series with it; without one it can draw too much current and destroy itself.^[8] Ohm's law alone cannot describe the LED (section 8 says why), but it works perfectly for the resistor:

1. Supply 5 V. Suppose the LED's datasheet gives a forward voltage of about 2.0 V, the voltage it takes while lit. The voltage left over for the resistor is the difference: 5 V − 2.0 V = 3.0 V.^[8]
2. Choose a current, say 10 mA (0.010 A), within the LED's rating.
3. R = V ÷ I = 3.0 V ÷ 0.010 A = 300 Ω. Resistors come in standard values, and the next one up is 330 Ω, which gives 3.0 V ÷ 330 Ω ≈ 9.1 mA.
4. Power in the resistor: 3.0 V × 0.0091 A ≈ 0.027 W, so a ¼ W part is plenty.

Article 14, LEDs and Optoelectronics, goes further, including what happens when the forward voltage varies.

7. Power: where the heat comes from

Power is the rate at which energy is converted, here from electrical energy into heat (or light, or motion). Its unit is the watt (W): one joule per second.^[5] For any part, the electrical power is the voltage across it times the current through it:^[9]

P = V × I

That is true for any part. For a resistor, you can substitute Ohm's law into it to get two more forms, handy when you know only two of the three quantities:^[9]

• Replace V with I × R: P = I × I × R = I²R (current squared, times resistance).
• Replace I with V ÷ R: P = V × V ÷ R = V²/R (voltage squared, divided by resistance).

All three give the same answer. For Example 1: 9 × 0.0409 ≈ 0.368 W; 0.0409² × 220 ≈ 0.368 W; and 9² ÷ 220 = 81 ÷ 220 ≈ 0.368 W (calculated). The squares matter: double the voltage across a resistor and the current doubles too, so the heat goes up four times.

Power ratings

Every resistor has a power rating, the most heat it can shed continuously without damage. Common through-hole resistors for hobby work are ¼ W; larger ones are rated ½ W, 1 W, 5 W and more.^[10] Exceed the rating and the resistor overheats; Ohmite lists drifting value, cracking, discoloration and, in severe cases, burning open as the results.^[11] SparkFun's example: an LED resistor carrying 0.544 W would make a ½ W resistor "get hot," so they suggest moving up to 1 W.^[10]

Even inside its rating, a resistor can be too hot to touch. KOA's datasheet for its metal oxide resistors shows the surface rising roughly 100 °C above the surrounding air for the 1 W size at full rated power, and the full rating applies only up to 70 °C ambient; above that, the allowed power falls (this is called derating).^[12] Ohmite, another resistor maker, advises choosing a rating with margin above the calculated power, allowing for hot enclosures and poor airflow.^[11] A simple habit, used by the calculator above, is to pick a rating at least twice the calculated power. That is this site's rule of thumb, not a standard; the datasheet is the authority. Article 3 covers this in more depth in Power: heat, and choosing a wattage.

8. When Ohm's law does not apply

Ohm's law is an empirical law: a pattern found by experiment, not a rule every material must obey. OpenStax compares it to Hooke's law for springs: it is not universally valid.^[3] Materials and parts that follow it, with a resistance that stays the same whatever the voltage and current, are called ohmic. Metal wires and ordinary resistors are ohmic.^[3]

Three common cases where it breaks down, or needs care:

• Temperature. The resistance of a metal rises as it warms.^[13] For most wires and resistors the change is small, but a lamp filament changes a lot.^[4] OpenStax's example is a car headlight: hot, it draws 2.50 A at 12.0 V, so R = 4.80 Ω; cold, its resistance is only 0.350 Ω, so for an instant it draws about 34 A.^[3]​^[9] Ohm's law holds at each moment, but R is not a fixed number.
• Diodes, LEDs and transistors. These are non-ohmic: their current does not rise in proportion to voltage at all. A diode passes almost nothing until its forward voltage is reached, then current rises steeply. That is why Example 5 applied Ohm's law to the resistor only. Article 6, Diodes, explains the curve.
• Changing current. In circuits where current changes quickly, capacitors and coils add effects that a plain resistance cannot describe. Articles 10 and 11, AC Circuits and RCL Circuits, extend the idea with a quantity called impedance.

9. Everyday uses

• Sizing resistors. LED resistors (Example 5), pull-up resistors (Example 2) and current limits for transistor bases are all one line of Ohm's law.
• Checking a design before you build. Work out the current from each supply and the power in each part. Article 9, DC Circuits, shows how to add these into a power budget for a whole circuit, and how the law combines with series and parallel rules.
• Troubleshooting. Measure the voltage across a resistor of known value and divide: that gives the current without breaking the circuit to insert an ammeter. A reading far from what Ohm's law predicts points to a wrong or damaged part.
• Wires and connections. Even a wire has some resistance, so a large current through it causes a voltage drop and heat. That is why heavy loads need thick wires, and why a short circuit is dangerous: a very low resistance lets a very large current flow.^[14]
• Regulators and protection. A linear voltage regulator burns off the difference between its input and output voltages as heat, power = voltage dropped × current; Article 15, Voltage Regulators, works through it. Fuses are chosen from the current a circuit should draw; see Fuses and Circuit Protection.

10. Safety

• Do not exceed a resistor's power rating. Calculate P first; an overloaded resistor can get hot enough to burn skin, scorch a board or fail open.^[10]​^[12] Allow margin.
• Never short a battery or supply. A wire straight across a battery has almost no resistance, so by I = V ÷ R the current becomes very large and the wire, and battery, heat fast.^[14] Lithium cells in particular can catch fire; see Article 13, Batteries and Cells.
• Your body follows Ohm's law too. The harm from a shock comes from the current through you, and that depends on the voltage and your body's resistance. OpenStax's example: a person with dry skin might have a resistance of about 200 kΩ, so 120 V drives only 0.6 mA; the same person soaking wet might be 10 kΩ, and the same 120 V drives 12 mA, above the level where muscles clamp and you cannot let go.^[14] Keep to low-voltage battery projects while learning, and leave wall (mains) wiring to qualified people.
• Measure safely. Measure resistance only with the power off, and never connect a meter set to measure current directly across a battery: an ammeter has very low resistance, so it acts as a short circuit.^[7]

The whole story in brief

• Voltage (V, volts) is energy per charge between two points; current (I, amperes) is charge per second; resistance (R, ohms, Ω) is the opposition to current.
• Ohm's law: V = I × R, so I = V ÷ R and R = V ÷ I. Convert to plain units first, or use volts, milliamperes and kilohms together.
• Power: P = V × I = I²R = V²/R, in watts. In a resistor it all becomes heat; stay well under the power rating.
• Limits: the law holds for ohmic parts like wires and resistors; diodes, LEDs and hot filaments do not follow a fixed R.

For the parts behind these numbers, see Resistors and DC Circuits; for reading circuit drawings, see the Schematic Symbols helper.

Sources

All links were checked in October 2026. External links open in a new tab.

1. OpenStax, College Physics 2e, section 20.1, "Current": https://openstax.org/books/college-physics-2e/pages/20-1-current
2. OpenStax, College Physics 2e, section 19.1, "Electric Potential Energy: Potential Difference": https://openstax.org/books/college-physics-2e/pages/19-1-electric-potential-energy-potential-difference
3. OpenStax, College Physics 2e, section 20.2, "Ohm's Law: Resistance and Simple Circuits": https://openstax.org/books/college-physics-2e/pages/20-2-ohms-law-resistance-and-simple-circuits
4. Tony R. Kuphaldt, Lessons In Electric Circuits, Volume I (DC), chapter 2, "Ohm's Law" (including "Nonlinear conduction"): https://www.ibiblio.org/kuphaldt/electricCircuits/DC/DC_2.html
5. NIST, Guide for the Use of the International System of Units (SI) (SP 811), chapter 4, "The Two Classes of SI Units and the SI Prefixes" (Tables 3 and 5): https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-4-two-classes-si-units-and-si-prefixes
6. SparkFun Learn, "Voltage, Current, Resistance, and Ohm's Law" tutorial (all pages): https://learn.sparkfun.com/tutorials/voltage-current-resistance-and-ohms-law/all
7. OpenStax, College Physics 2e, section 21.4, "DC Voltmeters and Ammeters": https://openstax.org/books/college-physics-2e/pages/21-4-dc-voltmeters-and-ammeters
8. SparkFun Learn, "Light-Emitting Diodes (LEDs)" tutorial (all pages): https://learn.sparkfun.com/tutorials/light-emitting-diodes-leds/all
9. OpenStax, College Physics 2e, section 20.4, "Electric Power and Energy": https://openstax.org/books/college-physics-2e/pages/20-4-electric-power-and-energy
10. SparkFun Learn, "Electric Power" tutorial (all pages; power ratings): https://learn.sparkfun.com/tutorials/electric-power/all
11. Ohmite, "Common Causes of Resistor Failure and How to Prevent Them" (blog, August 2026): https://www.ohmite.com/blog/2026/08/24/common-causes-of-resistor-failure-and-how-to-prevent-them
12. KOA Speer, MOS/MOSX "Reduced Size Metal Oxide Power Type Leaded Resistor" datasheet (derating curve and surface temperature rise chart; PDF): https://www.koaspeer.com/pdfs/MOS.pdf
13. OpenStax, College Physics 2e, section 20.3, "Resistance and Resistivity" (temperature coefficient of resistivity): https://openstax.org/books/college-physics-2e/pages/20-3-resistance-and-resistivity
14. OpenStax, College Physics 2e, section 20.6, "Electric Hazards and the Human Body": https://openstax.org/books/college-physics-2e/pages/20-6-electric-hazards-and-the-human-body