What is the DAC output voltage formula?

For an N-bit DAC with references V_min and V_ref, the output voltage is: V_out = V_min + (code × LSB), where LSB = (V_ref − V_min) / 2^N. Code ranges from 0 (outputs V_min) to 2^N − 1 (outputs V_ref − 1 LSB, just below full scale).

Why does code 2^N − 1 not reach V_ref exactly?

A DAC with N bits has 2^N steps but only 2^N − 1 intervals. The maximum code (all ones) produces V_ref − 1 LSB. To reach V_ref itself you would need the next code, which does not exist. This is called "missing full scale" and is expected behavior.

What is LSB size in a DAC?

LSB (Least Significant Bit) is the voltage increment produced by toggling the lowest bit. It equals (V_ref − V_min) / 2^N. A 12-bit DAC with a 3.3 V unipolar reference has an LSB of 3.3 / 4096 ≈ 0.806 mV.

How does a bipolar DAC differ from a unipolar one?

In a unipolar DAC V_min is 0 V, so the output spans 0 V to V_ref − 1 LSB. In a bipolar configuration V_min is negative (e.g. −5 V) and V_ref is positive (e.g. +5 V), so the output spans a symmetric or asymmetric range around 0 V. The formula is identical — only the reference values differ.

What limits the accuracy of a real DAC output?

Integral non-linearity (INL), differential non-linearity (DNL), gain error, offset error, and reference noise all limit real-world accuracy. The effective number of bits (ENOB) is typically 1–2 bits less than the nominal resolution.

What is the full-scale output of a DAC?

Full scale (FS) is V_ref − V_min, the entire voltage span the DAC can cover. The maximum achievable output is FS − 1 LSB. For a 10-bit unipolar 5 V DAC: FS = 5 V, max output = 5 V − (5 / 1024) ≈ 4.9951 V.

DAC Output Calculator

Enter DAC bit resolution, digital input code, and reference voltage to compute the analog output voltage, LSB size, and full-scale range.

DAC Parameters

Bit Resolution (N)

bits

Typical: 8, 10, 12, 16

V_min (lower reference)

Use 0 for unipolar (GND)

V_ref (upper reference)

Common: 3.3, 5, 2.5, 1.8

Digital Input Code

dec

Integer from 0 to 2^N − 1

Results

Output Voltage

—

LSB Size

—

Full-Scale Range

—

Output % of Span

—

Max Code

—

V_min — V_ref

Bar shows output voltage position within the full-scale span.

Formulas Used

LSB = (V_ref − V_min) / 2^N

V_out = V_min + code × LSB

Full-scale = V_ref − V_min

Output % = (code / (2^N − 1)) × 100

Code Sweep (key codes for your DAC)

Code (dec)	Code (hex)	Output Voltage	% of Span

Summary

A Digital-to-Analog Converter (DAC) maps an N-bit digital code to a proportional analog voltage between a lower and upper reference. The output voltage equals V_min plus the digital code multiplied by the LSB size, where the LSB equals the full-scale range divided by 2^N. This calculator accepts the bit resolution, digital input value, and reference voltage to instantly return the output voltage, LSB size, full-scale range, and the output expressed as a percentage of the full span.

How it works

Enter the DAC bit resolution (e.g. 12 for a 12-bit DAC).
Enter the lower reference voltage V_min (use 0 for a unipolar supply referenced to GND).
Enter the upper reference voltage V_ref (e.g. 3.3 V or 5 V).
Enter the digital input code — an integer from 0 to 2^N − 1.
Click Calculate to see the analog output voltage, LSB size, and full-scale range.
Use the sweep table to see how the output voltage changes across key digital codes.

Use cases

Verify the output voltage for a specific DAC code in a firmware design.
Choose the correct DAC bit depth for a required voltage step size.
Calculate the LSB voltage for audio DACs, signal generators, or motor controllers.
Design the output stage of a DAC-driven power supply or waveform generator.
Debug DAC mismatch between expected and measured output voltages.
Compare unipolar vs bipolar DAC output ranges for sensor driving applications.
Estimate the settling accuracy required for a given output tolerance.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu