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Volume Percentage Calculator

Converting a volume percentage to dB reveals why a slider's "50%" doesn't mean half as loud. This volume curve calculator compares three common volume curves — linear, squared (x²), and log dB — across the full 0–100% range. See the dB equivalent on each curve plus a rough perceived-loudness estimate.

Input

%
0 %50 %100 %
Current: 50 %
Common Slider Positions

Result

Decibels (selected curve)
—
dB
—
Amplitude factor
—
Power factor
—
Perceived loudness (≈)
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Linear curve
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Squared (x²)
—
Log dB (−60 dB floor)
—
Formulas
Linear: dB = 20·log₁₀(pct / 100)
Squared (x²): dB = 40·log₁₀(pct / 100)
Log dB: dB = −60 × (1 − pct / 100) — floor at 0% set to −60 dB
Perceived loudness ≈ 2^(dB / 10) × 100 % (Stevens-style approximation)
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Volume % → dB across all three curves
Linear Squared (x²) Log dB Y-axis clamped to −60 dB; result cards show un-clamped values.

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About Volume Curves & Perceived Loudness

A volume slider is not a percentage of loudness — it's a position on a curve that maps the slider knob to actual gain. Different devices and apps pick different curves, which is why "50% volume" on one device sounds very different from "50% volume" on another. The three curves on this page cover the most common cases.

Linear curve — rare in audio, common in tutorials

Maps slider position directly to amplitude: gain = pct / 100. So 50% = 0.5× the signal, which is −6 dB. Sounds "almost as loud" because amplitude has been halved but human loudness perception is logarithmic — a true "half as loud" requires roughly a 10 dB drop. Linear curves feel like the slider is "too top-heavy" — most of the audible range is crammed into the bottom 10%.

Squared (x²) curve — common in OS sliders

Maps slider to amplitude squared: gain = (pct / 100)². So 50% = 0.25× amplitude = −12 dB. This is closer to a perceptual taper but still front-loaded. Many consumer devices (older Android, some embedded systems) use this or its cousin x³ (cubed) because the math is cheap and the result is "good enough" without a true log lookup.

Log dB curve — the audio engineer's choice

Linear in dB: dB = floor × (1 − pct/100), with a chosen floor like −60 dB. So 50% = −30 dB, 75% = −15 dB, 25% = −45 dB. This log volume curve is used by pro audio mixers, DAW faders, and Apple/Windows newer volume sliders because it makes the slider feel evenly graduated to the ear. The same principle appears in physical hardware: an audio-taper potentiometer (also called a "log pot") uses a non-linear resistive track to approximate a −6 dB-per-half-turn feel, as opposed to a linear (B-taper) pot that most listeners find too jumpy at the top of its range. The trade-off is that there's no true "silence" position — 0% maps to whatever floor was chosen (usually −60 to −80 dB).

Perceived loudness — the ear isn't a meter

The "doubling of perceived loudness ≈ +10 dB" rule of thumb comes from psychoacoustic experiments (Stevens, Fletcher-Munson, Zwicker). It means a 50% slider on a log-dB curve (−30 dB) sounds roughly 1/8 as loud as full volume, not 1/2. The perceived loudness column on this page uses 2^(dB / 10) as a quick approximation — accurate enough for ballpark intuition, not for clinical loudness measurements. Streaming platforms (Spotify, YouTube, Apple Music) use LUFS (Loudness Units relative to Full Scale) rather than peak dB for normalization: Spotify targets −14 LUFS integrated, YouTube −13 LUFS, Apple Music −16 LUFS. Because LUFS accounts for the entire program material, not a single slider position, you cannot map a volume-slider percentage directly to a streaming loudness target — but you can use the amplitude-to-dB converter to explore how individual gain stages contribute to the final level.

Frequently Asked Questions

Why doesn't 50% volume sound half as loud?
Because the slider isn't a loudness percentage — it's a gain or dB position. And human loudness perception is logarithmic: roughly +10 dB = "twice as loud". For 50% to truly feel half as loud, the slider would need to map to −10 dB. On a linear curve, 50% = −6 dB (still ~66% as loud). On x², 50% = −12 dB (~44% as loud). On the log-dB curve, 50% = −30 dB (~12% as loud). None match "exactly half".
Which curve does my device use?
Hard to say without testing. Rough guide: Older Android / cheap speakers tend toward squared/cubed. iOS / modern macOS / Windows volume sliders use log-dB tapers. DAWs and pro audio always use log-dB faders. YouTube / web video players historically used linear, though many have moved to log. The best test: drop the slider from 100% to 50% — if it sounds "barely quieter" → linear; if it sounds "moderately quieter" → squared; if it sounds "much quieter" → log-dB.
What's the difference between amplitude factor and power factor?
Amplitude is the signal's voltage or sample value; power is amplitude squared. The dB scale uses ÷20 for amplitude and ÷10 for power. So at −6 dB amplitude factor = 0.5 (half), power factor = 0.25 (quarter). At −10 dB amplitude = 0.316, power = 0.1. This page's main dB value uses the amplitude convention (÷20) because that's what audio gain stages actually do — speakers and DACs care about voltage amplitude.
Why is the log-dB curve floor −60 dB and not −∞?
−∞ dB is mathematically silence (gain = 0), but a "0% maps to −∞" curve has a problem: the slider gets infinitely sensitive near the bottom. So real devices clamp the floor at something audible-but-very-quiet — usually −60 dB (one thousandth amplitude) or −80 dB. Below the floor, the device just outputs digital silence. If you want true silence, that's what the mute button is for.
How accurate is the perceived loudness estimate?
It's a rough rule of thumb, accurate to within a factor of 2 for normal music levels (60–90 dB SPL). The full picture uses equal-loudness contours (ISO 226) which vary with frequency, level, and listener. For clinical work, use LUFS (loudness units relative to full scale) or sone. For "is this slider position quiet, loud, or extremely loud?", the 2^(dB/10) approximation is fine.
Can I implement these curves in code?
Yes — they're all one-liners:
linear : gain = pct / 100
squared : gain = (pct / 100) ** 2
log dB : gain = 10 ** (floor * (1 - pct/100) / 20)
For Web Audio, set gainNode.gain.value = gain. For an integer DSP system, multiply your sample by gain (and watch for clipping/quantization).
What is an audio-taper potentiometer and how does it relate to these curves?
An audio-taper (or "log-taper") potentiometer uses a non-linear resistive track so that turning the knob halfway produces roughly −6 dB, not the −0 dB you'd get at the midpoint of a linear pot. This hardware approximation is why old volume knobs felt perceptually even even before software DSP existed. The "squared (x²)" curve on this page is the closest mathematical match to a typical audio-taper pot's actual behavior, though exact tapers vary by manufacturer.
What volume percentage equals half the perceived loudness?
It depends on the curve. For the ear to hear "half as loud," the gain must drop approximately −10 dB (Stevens power law). On a log-dB curve (floor −60 dB), −10 dB corresponds to about 83% of the slider range. On a squared (x²) curve, −10 dB ≈ 56%. On a linear curve, −10 dB ≈ 32%. In other words, with a log-dB slider you have to move surprisingly far down from the top before the audio sounds meaningfully quieter.
Why does my DAW fader show dB values instead of percentages?
DAW faders use dB directly because audio engineers think in decibels: gain staging, headroom, and signal-to-noise ratios are all expressed in dB. A percentage position would be ambiguous — it doesn't tell you the gain without also knowing the fader law. Most DAWs use a custom fader law (often −∞ at the bottom, 0 dB unity somewhere around 75–85% of the fader travel, and +6 to +12 dB clip region at the top) so that the "unity gain" position is easy to find by feel.

Related Tools

dB to Amplitude Converter
Decibels back to linear amplitude — the inverse of the curves on this page
Amplitude to dB Converter
Linear amplitude or voltage to decibels with voltage / power mode
Bit Depth Calculator
Dynamic range from bit depth — the noise floor that limits how low a volume curve can go
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