According to official sources such as the National Aeronautics and Space Administration's (NASA), the average distance between Neptune and the Sun is **4.5 billion kilometers (2.8 billion miles)** or 30 astronomical units. 

Neptune orbits around the sun in an elliptic manner. This ellipse is not a perfect circle, so the distance at a given point in time depends on Neptune's position. Therefore, the best estimate I can provide you with is an average, but I hope this answered your question.
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