Electrical & Electronics Calculators: Formulas and Examples
Every wiring question you will ever face comes back to four quantities: volts, amps, ohms and watts. These electrical & electronics calculators turn that electrical math into quick answers, so you can size a wire, price a load or check a resistor in seconds. Like most online electrical calculators, each one takes the values you know (voltage, current, a phase shift for AC circuits) and returns the missing value with its working.
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Electrical & Electronics Calculators Built on Ohm's Law
Ohm's law says the flow through a wire rises in direct proportion to the push behind it. It holds for any purely resistive load, in DC circuits and at any AC frequency, and it is the core of most electrical calculations:
$$V = I \times R \qquad I = \frac{V}{R} \qquad R = \frac{V}{I}$$The inverse of resistance is conductance, \(G = 1/R\), measured in siemens. A good ohms law calculator converts every input to base units first, so mixing kilohms with milliamperes never breaks the answer, and it shows the solution step-by-step.
Take a 9 V supply across a 470 Ω resistor: \(I = 9 \div 470 = 0.01915\) A, or 19.15 mA. Joule's law then gives the heat the part must shed: \(P = V^{2}/R = 81 \div 470 = \) 0.172 W, comfortably inside a ¼ W rating.
The Formula Wheel for Volts to Amps
The formula wheel puts P, I, V and R in the middle and lists three ways to reach each one from any two known values. To go from volts to amps, you need either the load in watts (\(I = P/V\)) or the load in Ω (\(I = V/R\)).
Electrical Power Calculator: Real Power, Apparent Power and Reactive Power
Wattage is the rate at which electrical energy moves through a load, measured in W. From grid generators run by the electric power industry to a single cell, an electrical power calculator uses three equivalent forms for DC and resistive loads:
$$P = V \times I = I^{2} \times R = \frac{V^{2}}{R}$$On AC, use RMS values and split the result in three. Apparent power \(S = V \times I\) is in VA; real power \(P = S \times PF\) is in W and does the work; reactive power \(Q = \sqrt{S^{2} - P^{2}}\) is in VAR and only sloshes back and forth.
Worked example: a heat pump draws 7.4 A on a 230 V circuit at a PF of 0.86. The calculator returns S = 1,702 VA, P = 1,463.72 W and Q = 868.52 VAR.
Power Factor and the Power Triangle
It is defined as \(PF = \cos\varphi = P/S\). In the power triangle, P is the base, Q the height and S the hypotenuse. For the heat pump, the phase angle is \(\cos^{-1}(0.86) = 30.68^{\circ}\). Inductive loads such as motors make current lag; capacitive loads make it lead.
Power Conversion and Energy Conversion Electrical Calculators
Most of a calculator index is power conversion: kilowatts to volt-amperes, joules to watts, BTU/h to W. The same few formulas cover a phone charger, LED lighting and a 2,000 W hair dryer.
Amps to Watts, Watts to Amps and kVA to kW
These unit conversions differ by phase and by PF:
| Conversion | Single phase | Three phase (line-to-line V) |
|---|---|---|
| Current to watts | \(P = PF \times I \times V\) | \(P = \sqrt{3} \times PF \times I \times V\) |
| Watts to current | \(I = P / (PF \times V)\) | \(I = P / (\sqrt{3} \times PF \times V)\) |
| kVA to kW | \(kW = kVA \times PF\) | \(kW = kVA \times PF\) |
kW to kWh, Electricity Bill and Energy Cost
Multiply the load by the hours it runs. The heat pump's 1.464 kW over 6.5 hours a day is 9.51 kWh; at $0.17 per kilowatt-hour that is $1.62 a day, or about $48.52 over 30 days. Add every appliance this way and you have an estimate of household energy consumption.
Voltage Drop Calculator and Wire Gauge Calculator Checks
Long runs lose volts in the wire itself. A single-phase voltage drop calculator uses the round-trip length:
$$V_{d} = \frac{2 \times L \times I \times R_{1000}}{1000}$$An 18 A load on 85 ft of 12 AWG copper (1.93 Ω per 1,000 ft) drops 5.91 V, or 4.92% of 120 V. Moving up to 10 AWG (1.21 Ω) cuts it to 3.70 V, or 3.09%. A wire gauge calculator also handles aluminum and circular mils, and corrects for temperature.
Wire Sizes, Conduit Sizing and the Grounding Conductor
A wire size calculator takes the load, insulation type, ambient temperature and number of wires and returns the gauge. The minimum wire is set by ampacity, which depends on metal and insulation ratings (60°C, 75°C, 90°C). It must be derated when ambient heat rises above 30°C or more than three wires share a raceway. Conduit sizing then follows from each wire's cross-sectional area and the allowed fill percentage, and the grounding conductor is read from a code table keyed to the overcurrent device's rating.
NEC Calculator Tools for Electricians and Electrical Contractors
Electricians, engineers and designers need answers that conform to the National Electrical Code. An NEC calculator works as a pocket electrical reference tool with the code tables built in: enter a 24 A continuous load and it applies the 125% rule to return a 30 A minimum overcurrent device. That speeds up estimating and helps avoid code violations. For safety, arc flash calculators estimate the hazard at a panel from fault level and clearing time, a study a general electrical calculator can't replace.
Motor Full-Load Amps and Breaker Sizes
A motor calculator looks up motor full-load amps from the horsepower, supply and phase you enter. From that figure it sizes the fuse or inverse-time circuit breaker, the overload protection and the NEMA starter sizes.
Electronic Formulas for Voltage Divider and Battery Calculators
The component side of the index works on parts rather than mains loads. Each calculator returns one figure:
- Voltage divider: enter the supply, R1 and R2 to get \(V_{out} = V_{in} \times R_{2}/(R_{1}+R_{2})\); 12 V across 3.3 kΩ and 1.8 kΩ gives 4.24 V.
- Parallel resistance: \(R = 1/(1/R_{1} + 1/R_{2})\), so 220 Ω and 330 Ω combine to 132 Ω.
- Battery capacity: charge in mAh × volts ÷ 1,000 gives Wh, so a 3,000 mAh cell at 3.7 V holds 11.1 Wh.