Distance for target sound level

What target-level distance means and what the response contains

Sound intensity from an ideal point source in free field spreads over a sphere whose surface area grows with the square of radius, so intensity is proportional to one over r squared. Sound pressure level in decibels is ten times the log of intensity over a reference intensity. The familiar transfer L two equals L one plus twenty log ten of r one over r two rearranges when the unknown is the range at a chosen level: r two equals r one times ten to the power of L one minus L target over twenty. That identity assumes spherical spreading, no ground reflections, no atmospheric absorption, and a source small compared with the distances involved; real rooms, barriers, and wind will shift the result, but the free-field estimate remains the standard first-order check for setbacks, permits, and textbook drills. This calculator returns the input level, reference distance, and target level; the solved distance; the signed delta_db from known level to target; the distance_ratio r two over r one; the precision used; a method tag inverse_square_target_distance; a short formula string; and a unit note that distance uses the same length unit as the reference. There is no Monte Carlo path and no weather model: the engine either evaluates the closed form inside the supported ranges or rejects the input with invalid_input. Rejected cases include missing level, reference distance, or target level; non-finite values; magnitudes above the documented ceilings; and any reference distance that is zero or negative, because the inverse-square intensity model is undefined at the source.

How levels and reference distance are read and how results stay reproducible

Distances must share a consistent length unit; metres are the usual choice, but any positive scale works because only the ratio with the reference enters the power-of-ten form. Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong setback. The preferred fields are level for the known sound pressure level in decibels, distance_from for the reference range r one, and target_level for the desired level at the unknown range, but aliases L1, spl, db, sound_level, and reference_level for level; r1, from, d1, distance1, and reference_distance for the reference; and L2, target, L_target, and desired_level for the target are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Zero or negative distance_from fails with invalid_input because zero distance is undefined under the inverse-square law. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for all numeric fields, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing ten to the power of delta L over twenty yourself.

Where target-level distance estimates fit in study, events, and software

On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.