Article — Ohm's Law / Resistance Calculator
Ohm's law and resistance calculator
Ohm's law states that voltage equals current times resistance: V = I × R. From any two of the three quantities you can solve the third, then derive electrical power through P = VI, P = I²R, or P = V²/R. The law holds for ohmic materials at constant temperature, which covers most metal resistors used in electronics.
Georg Simon Ohm published the relation in 1827 in his treatise on the galvanic circuit. The unit of resistance, the ohm (Ω), was named in his honor by the 1861 International Electrical Congress. Every working electrician, circuit designer, and physics student uses this law.
What Ohm's law says
The law links three measurable quantities. Voltage is the electrical potential difference between two points, measured in volts (V). Current is the rate of charge flow, measured in amperes (A) where 1 A = 1 coulomb per second. Resistance is the material's opposition to current flow, measured in ohms (Ω) where 1 Ω = 1 V/A.
Push more volts through a fixed resistor and current rises in direct proportion. Add resistance at the same voltage and current falls. The relationship is linear and constant for an ideal resistor at constant temperature, which is what makes it so practical for everyday circuit math.
Ohm's work was rejected by the German academic establishment of his time. He resigned his teaching post in protest. International recognition came in the 1840s and 1850s; the British awarded him the Copley Medal in 1841, well after the original paper.
The Ohm's law formula and its rearrangements
One equation, three useful forms.
V = I × R I = V / RR = V / I P = V × IP = I² × R P = V² / RWorked examples cover the three rearrangements:
- Find R — 12 V battery drives 0.5 A through a load. R = 12 / 0.5 = 24 Ω.
- Find I — 5 V supply with a 220 Ω resistor. I = 5 / 220 = 22.7 mA.
- Find V — 100 Ω resistor carrying 0.1 A. V = 100 × 0.1 = 10 V drop across the resistor.
Power and Ohm's law
Electrical power dissipated in a resistor equals voltage drop times current. From Ohm's law you can substitute to get three equivalent forms:
P = V × I when you know voltage and current directly. P = I² × R when you know current and resistance, common for series circuit analysis. P = V² / R when you know voltage and resistance, common for parallel circuit branch calculations.
A 1 kΩ resistor with 10 V across it dissipates P = V²/R = 100/1000 = 0.1 W. A 1/8 W resistor would overheat and fail; pick a 1/4 W part with at least a 2× margin. Surface-mount resistors at 0603 size are rated 0.1 W; through-hole 1/2 W axials handle 0.5 W; high-power chassis-mount resistors run 25 W and up.
A resistor with a 1/4 W rating run continuously at 0.25 W will burn out within months. Aim for 2× the calculated dissipation as a working margin, more if airflow is poor or ambient temperature is high. The body of a power resistor can reach 150 to 200 C in normal use.
Resistor color codes (IEC 60062)
Standard axial resistors use colored bands per IEC 60062. The 4-band system encodes two digits, a multiplier, and a tolerance.
Decode left to right: first digit, second digit, multiplier (power of 10), tolerance. Black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, gray = 8, white = 9. Gold multiplier = 0.1, silver = 0.01. Gold tolerance = 5%, silver = 10%.
Using Ohm's law to size an LED resistor
LEDs need current limiting because their forward voltage is nearly constant once they conduct. Without a resistor, even a small overvoltage drives unlimited current and destroys the part.
The math: subtract the LED forward voltage (Vf) from the supply, then divide by the target current. A red LED has Vf around 2.0 V and a safe current of 20 mA. On a 5 V Arduino pin: R = (5 - 2) / 0.020 = 150 Ω. Round up to the nearest E24 value (150 Ω exists) or use 180 Ω for a touch more headroom.
For a blue or white LED at Vf = 3.2 V driven from 5 V at 20 mA, R = (5 - 3.2) / 0.020 = 90 Ω. The standard value 100 Ω gives 18 mA, which is fine. Always pick the next standard value above the calculated R; lower R means more current.
Series and parallel resistance
Two resistors in series add. Two resistors in parallel combine as the product over the sum, or equivalently 1/Rtotal = 1/R1 + 1/R2.
- Series — same current through all, voltages add. Rtotal = R1 + R2 +...
- Parallel — same voltage across all, currents add. 1/Rtotal = sum of 1/Ri
- Two equal resistors in parallel — half the resistance. Two 10 kΩ gives 5 kΩ.
- Two unequal resistors in parallel — product over sum. 10 kΩ with 1 kΩ gives 909 Ω.
- Smallest dominates parallel — parallel total is always less than the smallest member.
Common Ohm's law mistakes
The law is simple. The errors come from edge cases and bad assumptions.
- Treating a diode like a resistor — semiconductor junctions have a curved V-I characteristic. Ohm's law gives a useful slope at a single operating point, not the full curve.
- Forgetting wire resistance — a 30 m run of 14 AWG copper has about 0.25 Ω. At 15 A that drops 3.75 V from a 120 V circuit, a 3 percent loss to ignore at your peril.
- Mixing milli and base units — 20 mA is 0.020 A. Plug 20 into the formula instead of 0.020 and you are off by 1,000.
- Ignoring temperature — copper resistance rises 0.39 percent per °C. A tungsten lamp filament has roughly 10× higher resistance hot than cold.
- Using Ohm's law with reactive AC loads — inductors and capacitors require V = IZ where Z is complex impedance. The simple form is for pure resistance only.