Engineering Reference

Electrical Power, Energy and RMS Reference

Quick-reference electrical power and energy units, DC and AC equations, watts versus watt-hours, real and apparent power, RMS, average, peak, ripple, ratings, and thermal terminology.

Reading Time: 13 min
Format: Quantity and formula lookup
Updated: September 24, 2026

Power Quantity and Unit Reference

Electrical power quantity and unit reference
Quantity	Symbol	Unit	Meaning	Common mistake
Voltage	V	volt (V)	Electrical potential difference	Do not mix RMS, peak and average definitions
Current	I	ampere (A)	Rate of charge flow	Continuous, RMS, average, peak and ripple are different
Real power	P	watt (W)	Average rate of real energy transfer	Not energy and not always equal to VA
Energy	E	joule (J), watt-hour (Wh)	Accumulated or transferred energy	W and Wh are not interchangeable
Apparent power	S	volt-ampere (VA)	Vrms × Irms for the defined AC condition	S − P is not heat loss
Reactive power	Q	var	Oscillatory energy exchange in sinusoidal steady state	Its standard power triangle is not universal for distorted waveforms
Power factor	PF	dimensionless	Real power divided by apparent power	PF is not efficiency
Efficiency	η	% or decimal	Output real power divided by input real power	Operating-point dependent; use 0.90, not 90, in decimal formulas
Power loss	Ploss	watt (W)	Input real power minus output real power	Load power is not automatically component heat
RMS value	Vrms / Irms	V / A	Root-mean-square value associated with heating effect	The peak/√2 rule applies only to a sinusoid
Peak value	Vpk / Ipk	V / A	Maximum instantaneous magnitude	Not a continuous or RMS rating
Ripple current	ΔI or Iripple	A	AC variation around an operating current	Define whether peak-to-peak, peak or RMS

Quick Formula Reference

Electrical power formula reference
Scenario	Formula	Conditions	Units	Caveat
Steady DC power	P = V × I	DC values, or compatible instantaneous/average definitions	V × A = W	Not a universal AC real-power equation
Resistive power	P = I²R	Resistive model with appropriate DC or RMS current	A² × Ω = W	Do not apply blindly to reactive loads
Resistive power	P = V²/R	Resistive model with appropriate DC or RMS voltage	V² / Ω = W	Requires the relevant resistance
Energy	E = P × t	Power appropriately constant or averaged over time	W × h = Wh	Varying power requires integration
Efficiency	η = Pout / Pin	Input and output are compatible average real powers	dimensionless	Efficiency varies with operating point
Loss	Ploss = Pin − Pout	Steady average real-power balance	W	Do not substitute VA for real input power
Single-phase apparent power	S = Vrms × Irms	Defined RMS voltage and current	VA	VA is not universally W
Single-phase real power	P = Vrms × Irms × PF	True PF for the measured waveform	W	For nonlinear loads PF is not simply cos φ
Sinusoidal reactive power	Q = Vrms × Irms × sin φ	Sinusoidal steady state	var	Do not generalize the simple triangle to arbitrary distortion
Balanced three-phase real power	P = √3 × VL × IL × PF	Balanced system using line-to-line voltage and line current	W	Do not substitute phase voltage without changing the formula
Sinusoidal RMS	Vrms = Vpk/√2; Irms = Ipk/√2	Pure sine wave only	V / A	Not valid for every waveform
Temperature rise	ΔT ≈ P × Rθ	Simplified steady-state effective thermal path	°C	Rθ depends on package, PCB, mounting and airflow

Power, Energy and Capacity Boundaries

Power is a rate

1 W = 1 J/s. Power transferred to a load is not automatically power dissipated as heat inside the source.

Energy accumulates over time

1 Wh = 3600 J, 1 kWh = 3.6 MJ, and 1 mWh = 3.6 J. W and Wh must not be interchanged.

Ah is charge, not energy

For approximately constant voltage, Wh ≈ V × Ah. Real battery voltage varies with chemistry, load and state of charge.

SI prefix case matters

m means milli, µ means micro, k means kilo and M means mega. For example, mW and MW differ by a factor of one billion.

Input, Output, Loss and Efficiency

Real-power balance

For a steady average boundary, Pin = Pout + Ploss. Use compatible real-power definitions at both ports.

Efficiency uses a decimal

η = Pout / Pin and Ploss = Pout(1/η − 1). Use 0.90, not 90, unless the equation explicitly expects percent.

Efficiency varies

Input voltage, output voltage, load, temperature, switching frequency, topology and operating mode change efficiency. A peak figure is not an all-load guarantee.

Loss categories differ

Conduction, switching, copper, core, ESR, gate-drive and control losses use different models. Do not apply I²R to every component or waveform.

AC Power and Power Factor

VA and W are different

S = VrmsIrms gives apparent power; P = S × PF gives real power. The numerical difference S − P is not heat loss.

PF is not efficiency

PF describes how effectively AC RMS voltage and current produce real input power. Efficiency compares output real power with input real power.

Displacement and true PF

For simple sinusoidal voltage and current, PF can equal cos φ. With nonlinear loads, waveform distortion also affects true PF.

Three-phase definitions matter

The √3 line formula shown above assumes a balanced system and uses line-to-line voltage and line current. Phase quantities require the corresponding form.

RMS, Average, Peak and Ripple

RMS is not average

RMS is based on the mean of the squared waveform and relates to resistive heating. A sine wave has zero signed average over a full cycle but nonzero RMS.

Peak-to-RMS depends on waveform

The division by √2 is valid for a pure sine wave. Square, triangular, pulsed and distorted waveforms require their actual RMS calculation.

Ripple needs a definition

Ripple may be specified as peak-to-peak, peak or RMS around an average operating point. Ripple current is not synonymous with load current.

Dynamic loads need multiple values

A pulsed or nonlinear load may require average power, RMS heating current and peak source capability to be checked separately.

Continuous, Peak and Surge Ratings

Power and current rating terminology
Rating	Meaning	Conditions to retain	Boundary
Continuous	Sustained operation	Temperature, cooling, mounting, lifetime and waveform	Not independent of thermal conditions
Peak	Maximum instantaneous or short-duration level	Duration and waveform definition	Not a continuous allowance
Pulse	Specified rectangular or defined transient	Pulse width, duty cycle and repetition	Different pulse conditions are not interchangeable
Surge	Exceptional short event	Event waveform, count, initial temperature and recovery	Not automatically repetitive
Transient	Time-limited excursion	Source impedance, duration and energy	Voltage and current maxima may not occur together
Derated	Reduced permitted operating level	Temperature, voltage, current, altitude or reliability requirement	No universal derating percentage applies

Derating and Thermal Interpretation

Headline power is conditional

A 100 W rating does not mean every board or ambient condition can dissipate 100 W continuously. Retain temperature, package, PCB, heatsink, mounting and airflow assumptions.

No universal derating percentage

Margin depends on transients, tolerance, temperature, altitude, lifetime, application standards and manufacturer guidance.

Thermal resistance is contextual

TJ ≈ TA + P × RθJA is a simplified steady-state model. RθJA includes the package and its specified test environment, not just the silicon.

Independent maxima do not combine

Maximum voltage, maximum current and maximum power commonly describe different conditions. Their arithmetic product is not an allowable operating point.

Worked Reference Examples

DC power

12 V × 2 A = 24 W for the stated steady DC condition.

Efficiency and loss

90 W / 0.90 = 100 W input; therefore Ploss = 10 W. The 90% value is an operating-point assumption.

DC input-current estimate

48 W / 0.90 = 53.33 W, then 53.33 W / 12 V = 4.44 A. This is average input current, not switching peak or ripple current.

Simplified thermal estimate

40°C + 2 W × 30°C/W = 100°C. Actual board conditions can differ substantially.

AC apparent and real power

230 Vrms × 2 Arms = 460 VA; at PF 0.8, P = 368 W. The 92 numerical difference is not device heat loss.

System and Datasheet Lookup Workflow

1Identify whether each quantity is DC or AC.
2Confirm voltage and current reference points.
3Distinguish average, RMS, peak and peak-to-peak values.
4Determine input real power, not only apparent power.
5Determine output power at the same operating point.
6Calculate efficiency and loss with consistent units.
7Separate power delivered to the load from device dissipation.
8Identify continuous, pulse, peak and surge ratings.
9Define ripple as RMS, peak or peak-to-peak.
10Check temperature, cooling and mounting conditions.
11Apply application-specific derating and transient requirements.
12Verify manufacturer footnotes, curves and test conditions.

Common Interpretation Mistakes

Confusing W with Wh.
Confusing Ah with Wh.
Treating efficiency as constant.
Entering 90 instead of 0.90 in a decimal formula.
Treating peak efficiency as all-load efficiency.
Treating VA as universally equal to W.
Confusing power factor with efficiency.
Treating S − P as heat loss.
Using peak/√2 for a non-sinusoidal waveform.
Confusing average, RMS and peak current.
Confusing ripple with load current.
Failing to define ripple as RMS, peak or peak-to-peak.
Treating peak or surge ratings as continuous.
Combining independent absolute maxima.
Ignoring derating and thermal conditions.
Treating RθJA as universal.
Confusing source output with source dissipation.
Assuming headline wattage applies under every condition.

Support reference

FAQ

What is the difference between watts and watt-hours?

Watts measure power, the rate of energy transfer. Watt-hours measure energy accumulated over time. One watt-hour equals 3600 joules.

What is the difference between ampere-hours and watt-hours?

Ampere-hours measure charge capacity; watt-hours measure energy. For an approximately constant voltage, Wh ≈ V × Ah, but battery voltage changes with chemistry, load and state of charge.

How do I calculate DC power?

For steady DC using compatible voltage and current definitions, P = V × I. For a resistive model, P = I²R or V²/R can also apply.

How is efficiency calculated?

Efficiency is η = Pout/Pin using compatible average real powers. Multiply by 100 for percent; use 0.90 rather than 90 in a decimal formula.

Is power-supply efficiency constant?

No. It can vary with input and output voltage, load, temperature, frequency, topology and operating mode. Peak efficiency applies only near its test point.

What is the difference between watts and VA?

Watts describe real power; VA describes apparent power. They are equal only when the relevant power factor is one.

Is power factor the same as efficiency?

No. Power factor relates AC real and apparent input power. Efficiency relates output real power to input real power.

What is RMS current?

RMS current is the square root of the mean squared waveform and relates to resistive heating. It is neither ordinary average nor peak current.

Is peak current the same as continuous current?

No. Peak, pulse and surge ratings require duration, duty-cycle, repetition and thermal conditions. They cannot automatically be used continuously.

What is ripple current?

Ripple current is the varying component around an operating current. A specification must identify whether it means RMS, peak or peak-to-peak ripple.

What does power derating mean?

Derating reduces an allowed operating level as temperature, voltage, cooling, altitude or reliability conditions change. Follow the component and application rules rather than one universal percentage.

Can maximum voltage and current ratings be used simultaneously?

Not automatically. Independent absolute maxima cannot generally be combined; power, SOA, thermal and transient limits must also be satisfied.

How does thermal resistance affect power dissipation?

A simplified steady-state rise is ΔT ≈ P × Rθ, but effective thermal resistance depends strongly on package, PCB copper, airflow, mounting and test conditions.

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