Enter the total alternating current voltage (volts) into the calculator to determine the DC Voltage from AC Voltage.
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DC Voltage from AC Voltage Formula
The following formula is used to calculate the DC Voltage from AC Voltage.
Vdc = Vac * .636
Variables:
- Where Vdc is the DC Voltage from AC Voltage (volts)
- Vac is the total alternating current voltage (volts)
To calculate DC voltage from AC voltage, multiply the AC voltage by .636.
| AC Voltage (V) | DC Voltage (V) |
|---|---|
| 1 | 0.636 |
| 2 | 1.272 |
| 3.3 | 2.099 |
| 5 | 3.180 |
| 6 | 3.816 |
| 9 | 5.724 |
| 10 | 6.360 |
| 12 | 7.632 |
| 15 | 9.540 |
| 18 | 11.448 |
| 20 | 12.720 |
| 24 | 15.264 |
| 30 | 19.080 |
| 36 | 22.896 |
| 48 | 30.528 |
| 60 | 38.160 |
| 90 | 57.240 |
| 120 | 76.320 |
| 170 | 108.120 |
| 325 | 206.700 |
| DC = 0.636 x AC (approximately 2/pi for a sine wave). | |
Where Does the 0.636 Factor Come From?
The 0.636 constant is not arbitrary. It equals 2/pi (2/3.14159 = 0.6366), which is the mathematical average of a full-wave rectified sine wave over one complete cycle. When an AC sine wave passes through a full-wave rectifier, the negative half-cycles are flipped to positive. Integrating the absolute value of sin(t) from 0 to pi and dividing by the period yields exactly 2/pi. This is the average (DC) component of the rectified waveform before any filtering or smoothing is applied.
For a half-wave rectifier, which only passes one half of the AC cycle, the average DC output drops to 1/pi (0.318) times the peak voltage, exactly half of the full-wave value. This distinction matters in circuit design: choosing half-wave vs. full-wave rectification directly determines the baseline DC voltage available to the load.
Rectifier Topologies Compared
Different rectifier circuits produce different DC output levels from the same AC input. The table below compares the four main rectifier types. All values assume silicon diodes with a 0.7 V forward drop.
| Topology | Diodes | Vdc (avg) | Loss | Ripple | PIV |
|---|---|---|---|---|---|
| Half-wave | 1 | 0.318xVp | 0.7V | 1x | Vp |
| FW center-tap | 2 | 0.636xVp | 0.7V | 2x | 2Vp |
| FW bridge | 4 | 0.636xVp | 1.4V | 2x | Vp |
| 3-ph bridge | 6 | 0.955xVp | 1.4V | 6x | Vp |
| Vp=Vrms x 1.414. Higher ripple freq = smaller cap needed. | |||||
The bridge rectifier is the most common topology in consumer power supplies because it achieves full-wave rectification without requiring a center-tapped transformer. The trade-off is two diode drops (1.4 V total) instead of one, which becomes significant at low output voltages.
Real-World DC Output After Filtering
The 0.636 factor gives the average DC voltage of an unfiltered rectified waveform. In practice, nearly all power supplies add a smoothing capacitor, which charges to the peak voltage minus diode drops rather than the average. The actual DC output of a filtered rectifier is substantially higher than 0.636 x Vpeak.
| AC | Vpeak | Avg DC | Filtered | Diff |
|---|---|---|---|---|
| 9V | 12.73V | 8.09V | 11.33V | +3.24V |
| 12V | 16.97V | 10.79V | 15.57V | +4.78V |
| 24V | 33.94V | 21.59V | 32.54V | +10.95V |
| 120V | 169.71V | 107.93V | 168.31V | +60.38V |
| 230V | 325.27V | 206.87V | 323.87V | +117V |
| Filtered DC=Vpeak-1.4V. Under load: Vripple=I/(2fC). | ||||
Ripple voltage depends on load current, capacitance, and rectification frequency. For a full-wave rectifier on 60 Hz (120 Hz ripple) drawing 1 A through 1000 uF: Vripple = 1/(2x120x0.001) = 4.17 V pk-pk. Doubling the cap halves the ripple.
Common AC-to-DC Conversions
| Use | AC | DC | Method | Eff |
|---|---|---|---|---|
| USB charger | 120/230V | 5V/2-3A | SMPS | 85-92% |
| USB-C PD | 120/230V | 20V/3-5A | GaN SMPS | 90-95% |
| LED driver | 120/230V | 30-50V | CC SMPS | 85-92% |
| PC PSU | 120/230V | 12/5/3.3V | LLC SMPS | 80-94% |
| Charger | 120/230V | 13.8-14.4V | Lin/SMPS | 60-88% |
| Arduino | 9-12V | 5V/0.5A | 7805 | 33-55% |
| VFD | 480V 3ph | 650-680V | 3ph bridge | 96-98% |
| Telecom | 120/230V | -48V | SMPS | 92-96% |
Switched-Mode vs. Linear Conversion
The 0.636 formula applies to basic rectification of a sine wave, the first stage in both linear and switched-mode power supplies. In a linear supply, the rectified DC passes through a regulator (78xx series or LM317) that dissipates excess voltage as heat. A 7805 producing 5 V from 12 V wastes 58% as heat.
Switched-mode supplies (SMPS) use high-frequency switching (50 kHz to 2 MHz) to convert voltage with far less waste. Modern GaN USB-C chargers switch above 500 kHz, enabling tiny transformers while achieving 93%+ efficiency. This is why modern chargers are far smaller than the linear wall-wart adapters of the 1990s and 2000s.
The 0.636 conversion factor represents the theoretical average DC from a full-wave rectified sine with no filtering. In a filtered supply, DC output approaches Vpeak minus diode drops, as the capacitor holds voltage near peak between cycles. The unfiltered average remains relevant for resistive loads driven directly by rectified AC, such as heater circuits or basic motor drives without capacitive filtering.
