Electric Resistance & Ohm's Law Calculator

Circuit Theory, Ohm's Law & Electric Resistance Metrology

Electric Resistance is the opposition offered by a substance to the flow of electric current:

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• Universal Electric Resistance Conversion Formulas (BIPM Standards)**:

1 MΩ = 10^3 kΩ = 10^6\ Ω = 10^9 mΩ = 10^12\ μΩ

1 kΩ = 1,000\ Ω = 10^6 mΩ = 0.001 MΩ

1 Statohm (statΩ) = 8.987552 × 10^11\ Ω | 1 Abohm (abΩ) = 10^-9\ Ω

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• Conductance, Ohm's Law & Johnson Noise Equations**:

G = (1) / (R) (Conductance in Siemens, S Mhos )

I = (V) / (R) (Amperes) | P = (V^2) / (R) = I^2 × R (Watts)

v_n = √(4 k_B T R Δ f) (Johnson-Nyquist Thermal Noise in Volts RMS)

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• Standard Resistance & Impedance Benchmarks**:

• Current Sense Shunt: 10.0 mΩ 0.010\ Ω V_drop = 100 mV @ 10A

• Audio Loudspeaker: 8.0\ Ω G = 125.0 mS 100W @ 28.3V

• Human Skin Contact: 1,000.0\ Ω 1.0 kΩ I = 120 mA @ 120V (Shock hazard)

• Pull-Up Resistor: 10.0 kΩ 10,000\ Ω I = 0.50 mA @ 5V P = 2.5 mW

• Transformer Megger Test: 10.0 GΩ = 10,000 MΩ I_leak = 100 nA @ 1kV

How to Use This Calculator

Enter your Electric Resistance (R) (e.g. 10 in R), From Electric Resistance Unit — choose from Kilohms (kΩ = 1,000 Ω - Electronics / Pull-Up), Ohms (Ω = V/A - SI Base Unit), Megohms (MΩ = 10⁶ Ω - High-Z Probes / Insulation), To Electric Resistance Unit — choose from Ohms (Ω), Kilohms (kΩ), Megohms (MΩ), Applied Circuit Voltage (V in Volts) (e.g. 5.0 in V), Noise Bandwidth (Δf in Hz, 20kHz Audio) (e.g. 20000 in Hz), and Circuit & Component Benchmark — choose from Custom Resistance Component, I2C / GPIO Pull-Up Resistor (10.0 kΩ @ 5V) → 10,000 Ω | I = 0.50 mA | P = 2.50 mW | G = 100 µS | Johnson Noise = 1.80 µV, Hi-Fi Audio Loudspeaker (8.0 Ω @ 28.3V = 100W) → 0.0080 kΩ | I = 3.54 A | G = 125.0 mS. Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Multipliers to SI Base Unit Ohms (Ω = V/A)

Johnson-Nyquist Thermal Noise: v_n = sqrt(4 k_B T R delta_f)

Worked Example

An embedded systems engineer placing a 10 kΩ pull-up resistor on a 5V I2C bus line calculates that when pulled low, the resistor conducts 0.50 mA and dissipates 2.5 mW, well within the 125 mW rating of an 0805 SMD resistor.

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