Ohm's law and power calculator: resistivity, AWG and mm²

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How do you calculate voltage, current, resistance and power using Ohm's law? How do you calculate the resistance of a cable knowing its material, length and cross-sectional area? Here is a complete, simple and fast Ohm's law calculator that you can use directly online.

The first calculator lets you determine voltage V, current I, resistance R and power P from two known values. The second applies Ohm's second law to conductors and also lets you convert the cross-sectional area between AWG and mm², also commonly indicated as mmq.

How does the online Ohm's law calculator work?

The calculator is divided into two sections. The first calculates voltage, current, resistance and power. The second calculates conductor resistance, resistivity, length and cross-sectional area and also includes AWG/mm² conversion.

In the first calculator, enter two values and leave the other two blank. In the second, enter three values and leave blank the one you want to calculate.

You can use either a comma or a period as the decimal separator. Do not use a comma and a period together in the same number.

Ohm's first law: voltage, current and resistance

Ohm's first law relates voltage V applied to a resistive component, current I flowing through it, and resistance R.

V = R × I

I = V / R

R = V / I

Knowing any two of the three quantities allows the third to be calculated immediately.

The calculator works with positive values and magnitudes. It is intended primarily for DC circuits and resistive loads.

For AC circuits that include inductance, capacitance, reactance, or a power factor other than 1, the relationships for impedance and AC power must be used.

Calculate power with Ohm's law

The electrical power P absorbed or dissipated by a resistive load can be calculated from voltage and current.

P = V × I

Combining this relationship with Ohm's law also gives:

P = I² × R

P = V² / R

The calculator can therefore start from any compatible pair of V, I, R and P.

All combinations supported by the voltage, current, resistance and power calculator

• voltage V and current I to calculate resistance R and power P
• voltage V and resistance R to calculate current I and power P
• voltage V and power P to calculate current I and resistance R
• current I and resistance R to calculate voltage V and power P
• current I and power P to calculate voltage V and resistance R
• resistance R and power P to calculate voltage V and current I

Ohm's second law: conductor resistance

Ohm's second law allows the electrical resistance of a homogeneous conductor with uniform cross-sectional area to be calculated from the material resistivity, conductor length and cross-sectional area.

R = ρ × L / S

In the calculator, R is expressed in ohms, ρ in Ω·mm²/m, L in meters and S in square millimeters. Using resistivity directly in Ω·mm²/m means that the cross-sectional area does not need to be converted from mm² to m².

The inverse formulas used by the calculator are:

ρ = R × S / L

L = R × S / ρ

S = ρ × L / R

Resistivity of copper

In the calculator menu, the material is simply listed as Copper, which is the most useful designation in practical use. The calculator uses ρ = 0.017241 Ω·mm²/m at 20 °C. This is the reference value of the International Annealed Copper Standard (IACS), historically used as the reference for the conductivity of copper intended for electrical applications.

This does not mean that every real copper wire has exactly this resistivity. Purity, treatment, temperature and conductor construction can cause differences from the reference value.

Resistivity of aluminum

For aluminum, the menu simply uses the name Aluminum. However, there is no single resistivity value valid for every commercial aluminum product. The preset uses ρ = 0.028126 Ω·mm²/m at 20 °C as a documented conservative value for 1350 aluminum intended for electrical conductors.

For design calculations, it is preferable to use the resistance per unit length or resistivity specified by the manufacturer of the actual cable being used.

Resistivity depends on temperature

Electrical resistivity depends on temperature. In common metallic conductors, resistance normally increases as temperature increases.

For electrical conductor characteristics, 20 °C is commonly used as the reference temperature. The IACS copper reference is also defined at 20 °C.

The calculator does not automatically compensate resistivity for temperature. If the conductor operates at a temperature significantly different from the reference temperature, or if greater accuracy is required, use the appropriate temperature coefficient or the data provided by the manufacturer.

For IACS standard copper, the temperature coefficient of resistance at 20 °C is approximately 0.00393 per degree Celsius. This value must not be applied automatically to other materials.

Resistivity of some pure metals

The calculator also includes several pure metals for comparison, exercises and special applications. In these cases, bulk reference values at room temperature are used.

Silver: ρ ≈ 0.01587 Ω·mm²/m.

Gold: ρ ≈ 0.02214 Ω·mm²/m.

Tungsten: ρ ≈ 0.0528 Ω·mm²/m.

Molybdenum: ρ ≈ 0.0534 Ω·mm²/m.

Nickel: ρ ≈ 0.0693 Ω·mm²/m.

Platinum: ρ ≈ 0.106 Ω·mm²/m.

These values are provided as comparison references and should not be interpreted as guaranteed characteristics of any commercial wire or component. Purity, crystal structure, processing, defects and temperature can affect actual resistivity.

AWG mm² converter: from American Wire Gauge to square millimeters

AWG stands for American Wire Gauge and is a system used mainly in North America to identify electrical conductor sizes. It is also common in documentation for electronics, automotive applications, audio equipment, power supplies, batteries and equipment of American origin.

The AWG scale is not linear. As the AWG number increases, conductor diameter and cross-sectional area decrease.

The geometric definition uses a diameter of 0.127 mm for AWG 36. The diameter ratio between AWG 4/0 and AWG 36 is 92, geometrically divided into 39 intervals.

For an AWG number n, the nominal diameter of the equivalent solid conductor can be calculated with the formula:

d = 0.127 × 92^((36 − n) / 39) mm

The corresponding geometric cross-sectional area is:

S = π × d² / 4

The calculator selector includes sizes from AWG 4/0 through AWG 40.

Convert from AWG to mm²

To convert from AWG to mm², simply select an AWG size. The calculator automatically calculates the corresponding nominal geometric cross-sectional area and enters it in the Cross-sectional area S field.

The resulting cross-sectional area can also be used directly in the Ohm's second law calculation.

Convert from mm² or mmq to AWG

The calculator can also be used in the reverse direction. When a cross-sectional area in mm² is entered, the calculator determines the equivalent theoretical AWG number and the standard AWG size with the closest cross-sectional area.

It is important to distinguish between the two results. A metric cross-sectional area does not necessarily correspond exactly to an integer AWG size.

For example, a cross-sectional area of 2.5 mm² corresponds mathematically to approximately AWG 13.21. The standard AWG size with the closest cross-sectional area is AWG 13, which has an area of approximately 2.624 mm².

Table of selected AWG to mm² conversions

• AWG 18 ≈ 0.823 mm²
• AWG 16 ≈ 1.309 mm²
• AWG 14 ≈ 2.081 mm²
• AWG 13 ≈ 2.624 mm²
• AWG 12 ≈ 3.309 mm²
• AWG 10 ≈ 5.261 mm²
• AWG 8 ≈ 8.366 mm²
• AWG 6 ≈ 13.302 mm²
• AWG 4 ≈ 21.151 mm²
• AWG 2 ≈ 33.631 mm²
• AWG 1/0 ≈ 53.475 mm²
• AWG 2/0 ≈ 67.431 mm²
• AWG 3/0 ≈ 85.029 mm²
• AWG 4/0 ≈ 107.219 mm²

AWG, stranded cables and outer diameter

AWG/mm² conversion concerns the nominal conductor cross-sectional area and does not directly provide the outer diameter of an insulated cable.

In stranded conductors, the helical arrangement and number of strands affect the physical diameter of the bundle. Insulation further increases the cable's outer diameter.

The actual resistance of a stranded cable may also differ slightly from the ideal value obtained using only resistivity, length and geometric area. When available, use the manufacturer's specified resistance per unit length for real design work.

Ohm's law and automotive cable sizes

Ohm's second law is also useful for evaluating the resistance of automotive wiring. In this field, conductor sizes are commonly expressed in both mm² and AWG, especially for accessories, components and wiring of American origin.

Copper is commonly used in vehicle electrical wiring. Aluminum is also used in some applications, especially where reducing wiring harness weight is important.

Tinned copper is used in applications where greater corrosion protection is useful. It is not offered as a separate material in the calculator because the main conductor remains copper and actual resistance depends on the specific cable construction.

Cable length: outgoing and return paths

In the formula R = ρ × L / S, L is the electrical length of the conductor whose resistance is being calculated.

If a circuit uses a 5-meter outgoing conductor and an identical 5-meter return conductor, the total resistance of the two conductors must be calculated using L = 10 m.

In automotive applications, current may instead return through the vehicle body or chassis. In this case, the cable length should not be doubled automatically, because the ground return path has different characteristics and includes connection points and contact resistances.

Example calculation using Ohm's first law

Consider a 6 Ω resistor supplied at 12 V.

I = V / R

I = 12 / 6 = 2 A

The dissipated power is:

P = V × I

P = 12 × 2 = 24 W

Example: resistance of a copper cable

Consider a 10-meter copper conductor with a cross-sectional area of 2.5 mm². Using the IACS reference resistivity at 20 °C:

ρ = 0.017241 Ω·mm²/m

R = ρ × L / S

R = 0.017241 × 10 / 2.5

R = 0.068964 Ω

If the same connection uses two identical 10-meter conductors, one outgoing and one return, the total conductor length is 20 meters.

R = 0.017241 × 20 / 2.5 = 0.137928 Ω

Example comparison between copper and aluminum

Consider two 10-meter conductors with the same cross-sectional area of 2.5 mm².

Using the copper reference at 20 °C gives approximately 0.068964 Ω.

Using 0.028126 Ω·mm²/m for aluminum gives approximately 0.112504 Ω.

For the same length and cross-sectional area, the aluminum conductor in this example therefore has significantly higher resistance than the copper conductor.

Limits of cable resistance calculations

Ohm's second law gives the theoretical resistance of the conductor material based on resistivity, length and cross-sectional area.

The result does not automatically include the resistance of terminals, cable lugs, connectors, joints, crimps, solder joints, ground points, oxidation or other contacts present in the actual circuit.

The calculation also assumes homogeneous material and a uniform cross-sectional area along the entire length considered.

Cable cross-sectional area alone does not determine maximum current

AWG/mm² conversion and Ohm's second law must not be used alone to determine a cable's maximum allowable current.

Ampacity also depends on conductor material, insulation, ambient temperature, maximum permitted temperature, installation method, ventilation, grouping with other cables and applicable standards.

For final sizing of an electrical system or wiring harness, use the manufacturer's technical data and the criteria required for the specific application.

All calculations you can make with this online calculator

• calculate voltage V given current I and resistance R
• calculate current I given voltage V and resistance R
• calculate resistance R given voltage V and current I
• calculate power P given voltage V and current I
• calculate voltage and power given current and resistance
• calculate current and resistance given voltage and power
• calculate voltage and resistance given current and power
• calculate voltage and current given resistance and power
• calculate the resistance of a conductor with R = ρ × L / S
• calculate resistivity ρ
• calculate length L
• calculate cross-sectional area S in mm²
• convert AWG to mm²
• convert mm² or mmq to the equivalent theoretical AWG
• identify the standard AWG size with the closest cross-sectional area
• calculate using the copper reference at 20 °C
• calculate using a reference value for aluminum conductors
• compare silver, gold, tungsten, molybdenum, nickel and platinum
• use a custom resistivity

Technical references used

For copper, the reference used is the International Annealed Copper Standard reported in the Copper Wire Tables of the National Bureau of Standards, now NIST.

For the reference aluminum used for electrical conductors, the 20 °C resistivity values in ASTM B233 for 1350 aluminum were considered.

AWG conversion is calculated directly from the geometric definition of American Wire Gauge given in NBS/NIST tables, rather than from a simple table of rounded equivalents.

The bulk resistivity values for silver, gold, tungsten, molybdenum and nickel are literature values for elemental metals at room temperature. The platinum value is a NIST reference value at approximately 300 K.

For an actual commercial component, cable or material, the manufacturer's specified data always take precedence.