ERR Quantization Accuracy

Quantization Error Calculator

Calculate the difference between an original real value and its quantized or dequantized approximation. Measure signed error, absolute error, relative error and percentage error.

Absolute Error Signed Error Relative Error Percentage Error

Quantization Error Error Analysis

Original Value Original real or reference value.

Quantized / Dequantized Value Approximate value after quantization and reconstruction.

Signed error = approximate – original
Absolute error = |approximate – original|
Relative error = absolute error / |original|

Quantization Error Result

–

Original Value –

Approximate Value –

Signed Error –

Absolute Error –

Relative Error –

Percentage Error –

Error Direction –

Exact Match –

What Is Quantization Error?

Quantization error is the numerical difference introduced when a value is represented using a limited set of discrete levels instead of its original higher-precision value.

When a real value is quantized and later reconstructed, the result may not exactly equal the original value. The difference between the two values is the quantization error.

Signed Quantization Error

Signed error preserves the direction of the difference:

Signed error = approximate value – original value

A positive result means the approximation is higher than the original value. A negative result means it is lower.

Absolute Quantization Error

Absolute error measures only the size of the difference and ignores direction.

Absolute error = |approximate – original|

For example:

Original = 1.25
Approximate = 1.30

Absolute error = |1.30 – 1.25|
= 0.05

Relative Quantization Error

Relative error expresses the absolute error in relation to the magnitude of the original value.

Relative error = absolute error / |original value|

This makes it easier to compare the significance of an error across values of different sizes.

Percentage Quantization Error

Percentage error expresses relative error as a percentage.

Percentage error = relative error × 100

Using an original value of 1.25 and an approximate value of 1.30:

Absolute error = 0.05

Relative error = 0.05 / 1.25 = 0.04

Percentage error = 4%

Positive and Negative Quantization Error

The sign of the error shows whether the quantized approximation overshoots or undershoots the original value.

Original = 10
Approximate = 10.2
Signed error = +0.2

Approximation is above the original.

Original = 10
Approximate = 9.8
Signed error = -0.2

Approximation is below the original.

What Happens When the Original Value Is Zero?

Relative and percentage error use the magnitude of the original value as the denominator. When the original value is zero, division by zero is undefined.

In that case, this calculator still reports signed and absolute error, but relative and percentage error are shown as undefined unless the values match exactly.

Why Quantization Error Matters

Quantization reduces numerical precision by mapping values to a finite set of representable levels. Measuring error helps determine how closely the lower-precision representation approximates the original data.

This is relevant in digital signal processing, numerical computing, data compression, embedded systems and low-precision machine-learning workflows.

Quantization Error and AI

Low-bit numerical formats such as INT8 and INT4 can reduce model storage and computational requirements, but quantized parameters may differ from the original floating-point values.

Quantization error provides a direct way to inspect how much numerical deviation has been introduced for an individual value.

Important Quantization Error Notes

Important: this calculator measures error only.

It does not calculate quantization scale or zero point.

It does not convert the original value into INT8, INT4 or another quantized representation.

Signed error preserves whether the approximation is above or below the original.

Absolute error reports only the magnitude of the difference.

Relative and percentage errors are undefined when the original value is zero, except when both values are exactly zero.

Quantization Error Calculator FAQs

What is quantization error?

Quantization error is the difference between an original numerical value and the value represented after quantization or reconstruction.

How is signed quantization error calculated?

Signed error equals the approximate value minus the original value.

How is absolute quantization error calculated?

Absolute error is the absolute value of the difference between the approximate and original values.

What is relative quantization error?

Relative error is the absolute error divided by the magnitude of the original value.

How do I calculate percentage quantization error?

Multiply relative error by 100.

What does positive quantization error mean?

It means the approximate value is greater than the original value.

What does negative quantization error mean?

It means the approximate value is less than the original value.

What does zero quantization error mean?

It means the approximate value exactly matches the original value.

Can relative error be calculated when the original value is zero?

No. Relative error requires division by the magnitude of the original value, so it is undefined when that value is zero.