ElectricalMulti-SolverDC Circuit

DC Power & Ohm's Law Matrix

A universal DC circuit solver that resolves voltage, current, resistance, and power from any two known electrical variables, with additional engineering estimates for conductor selection, voltage drop, resistor thermal loading, and battery runtime.

Known Variables Setup

V

Electrical potential difference

A

Charge flow rate

Ω

Electrical opposition

W

Electrical power

Live DC Circuit Model

I = 2.00 A+DC SOURCE12.00 V6.00 ΩP = 24.00 W+−
Circuit solution active
DC · Resistive Load

Matrix Outputs

Resolved

Voltage (V)

12.00V

Current (I)

2.00A

Resistance (R)

6.00Ω

Power (P)

24.00W

V × I

24.00 W

I² × R

24.00 W

V² / R

24.00 W

Conductor

Estimated AWG

18 AWG

Thermal

Dissipation

24.00 W

Runtime

Battery

21.3 h

Resistor Thermal Analysis

Compare calculated dissipation against component rating.

W

Maximum nominal package dissipation

Actual Dissipation

24.00 W

Thermal FoS

2.08

Calculated electrical power is below the specified nominal resistor rating with a reasonable margin.
m

Physical source-to-load distance

Load Voltage

11.58 V

Voltage Loss

3.5%

Cable resistance0.2100 Ω
Voltage drop0.420 V

Battery Capacity

Nominal capacity available to the load.

Ah

Nominal battery capacity

Estimated Runtime

21.3 h

Load Current

2.00 A

01 / Thermal Engineering

Joule Heating & Component Derating

Electrical power dissipated by a resistive load appears as heat. Component ratings therefore need sufficient margin above calculated operating power.

Engineering note

Resistor power ratings are normally specified under particular ambient and mounting conditions. Actual permissible dissipation can be lower at elevated ambient temperatures or inside enclosed assemblies.

02 / Cabling & Loss

Conductor Estimation & Voltage Drop

Cable resistance increases with conductor length. The resulting voltage drop reduces the voltage available at the load.

Conductor Note

Approximate continuous-current sizing estimate. Actual conductor selection must account for installation method, insulation, ambient temperature, bundling and applicable electrical codes.

03 / System Simulation

Battery Runtime

Estimate operating time from battery capacity and calculated load current.

Model limitation

Runtime is an approximate capacity/current estimate with an 85% usable-capacity factor. It does not model a full Peukert curve, battery chemistry, temperature, aging, discharge-rate dependency or BMS cutoff.

04 / Mathematical Roots

Algorithm & Core Equations

The solver derives the remaining electrical variables from any two independent known values.

Governing Formula

V = I times R
VVolts

Voltage

IAmps

Current

ROhms

Resistance

Governing Formula

P = V times I = I2R = frac{V2}{R}
PWatts

Power

VVolts

Voltage

IAmps

Current

ROhms

Resistance

TypeScript — Universal DC Solver
type KnownCombo = 'VR' | 'VI' | 'VP' | 'IR' | 'IP' | 'RP';

function solveDCMatrix(
  known: KnownCombo,
  val1: number,
  val2: number
) {
  let V = NaN;
  let I = NaN;
  let R = NaN;
  let P = NaN;

  switch (known) {
    case 'VR':
      V = val1;
      R = val2;
      I = V / R;
      P = V * I;
      break;

    case 'VI':
      V = val1;
      I = val2;
      R = V / I;
      P = V * I;
      break;

    case 'VP':
      V = val1;
      P = val2;
      I = P / V;
      R = (V * V) / P;
      break;

    case 'IR':
      I = val1;
      R = val2;
      V = I * R;
      P = I * I * R;
      break;

    case 'IP':
      I = val1;
      P = val2;
      V = P / I;
      R = P / (I * I);
      break;

    case 'RP':
      R = val1;
      P = val2;
      V = Math.sqrt(P * R);
      I = Math.sqrt(P / R);
      break;
  }

  return { V, I, R, P };
}

Engineering Scope & Limitations

Ohm's Law

The core solver assumes a linear resistive DC relationship between voltage, current and resistance.

Cable Sizing

AWG selection is an estimation and should not replace code-compliant conductor sizing for real installations.

Battery Runtime

Runtime is an approximate engineering estimate rather than a battery-management or electrochemical simulation.

DC Power & Ohm's Law Matrix — Technical Reference

What This Ohm's Law Calculator Solves

This DC power calculator is a two-parameter solver for linear resistive circuits. Rather than requiring you to pick a single unknown, it accepts any two of the four fundamental DC quantities — voltage (V), current (I), resistance (R), or power (P) — and returns the remaining two. That makes it a universal voltage-current-resistance solver rather than a one-directional Ohm's Law calculator. The underlying model is a steady-state, linear, resistive DC network governed by Ohm's Law and Joule's Law.

Governing Equations

The solver is built on two relationships. Ohm's Law relates voltage, current, and resistance:

V = I × R

Joule's Law relates power to the other three quantities:

P = V × I = I2R = V2/R

Here V is in volts, I in amperes, R in ohms, and P in watts. The three forms of the power equation are algebraically identical; which one the solver uses depends on which pair of inputs is known. For example, given I and R, power is computed as I2R; given V and R, power is computed as V2/R.

Calculation Method

The solver is a deterministic case switch over the six possible known pairs — VR, VI, VP, IR, IP, and RP. For each case, the two known values are substituted into the governing equations and the remaining two are derived algebraically. The engineering sequence is:

  1. Select the two known quantities and enter their values.
  2. The solver identifies the correct case branch.
  3. It applies Ohm's Law to find the missing electrical quantity.
  4. It applies the appropriate form of P = VI = I2R = V2/R to find power.
  5. It reports V, I, R, and P as a consistent set.

Because the inputs are algebraically independent, any consistent pair produces a unique solution. Inconsistent or physically invalid pairs (for example, V = 0 with P > 0) are not meaningful and should not be used.

Input Parameters

Voltage (V) is the potential difference across the element, in volts. It drives current through the resistance.

Current (I) is the rate of charge flow, in amperes. For a fixed resistance, doubling current quadruples dissipated power.

Resistance (R) is the opposition to current flow, in ohms. It is assumed constant over the operating range.

Power (P) is the rate of energy dissipation, in watts. In a purely resistive DC load, all of this power appears as heat.

A common mistake is mixing units — for example, entering milliamps as amps or kilohms as ohms. Always convert to base SI units before interpreting the result.

Engineering Interpretation

The solved set of V, I, R, and P is the starting point for several downstream checks that this page also estimates. Power dissipation determines the thermal load on a resistor and therefore the required power rating; a resistor operated near its rated wattage without derating can drift or fail. Current drives conductor selection: the AWG estimate converts continuous current into an approximate wire gauge, while the voltage-drop estimate accounts for the resistance of the conductor run itself. For battery-powered systems, the load current feeds an approximate runtime estimate based on capacity and an assumed usable-capacity fraction.

These are engineering estimates, not design certifications. A calculated operating point does not by itself confirm that a component, conductor, or assembly is safe or code- compliant.

Units and Conversion

The solver works in base SI units: volts, amperes, ohms, and watts. Useful conversions include 1 A = 1000 mA, 1 kΩ = 1000 Ω, 1 kW = 1000 W, and 1 V = 1000 mV. Because P = I2R is quadratic in current, small unit errors in current have a disproportionate effect on the computed power.

Assumptions and Limitations

  • The circuit is treated as a single linear resistive DC element.
  • Resistance is assumed constant and independent of temperature and current.
  • Steady-state conditions are assumed; no transient, capacitive, or inductive effects are modelled.
  • The conductor estimate is an approximation and does not account for insulation temperature rating, ambient temperature, bundling, or installation method.
  • Battery runtime is a simple capacity/current estimate with a fixed usable-capacity factor, not an electrochemical or Peukert-corrected model.
  • No safety factor, code compliance, or design verification is implied by the output.

Practical Engineering Use

This DC power and Ohm's Law calculator is useful for quick sanity checks during electrical and electronics work: sizing a series resistor for an LED, estimating the dissipation in a load resistor, checking the current draw of a DC motor or heater, choosing a rough AWG gauge for a low-voltage run, or estimating how long a battery will last at a given load. It is intended as a fast first-pass tool, with detailed thermal, cabling, and battery analysis left to dedicated design procedures.

Continue Calculating

built

Ohms Law

Quickly calculate and analyze parameters for your ohms law requirements.

Open
built

Pcb Trace Calculator

Quickly calculate and analyze parameters for your pcb trace calculator requirements.

Open
built

Ugv 4Wd Platform

Quickly calculate and analyze parameters for your ugv 4wd platform requirements.

Open