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Physics

Power Ratio to dB

10 log₁₀(ratio). Free online Power Ratio to dB. Calculate power ratio to db online — fast, accurate, mobile-friendly, no signup needed.

dB (power)
20
dB (voltage)
40

Derivation

  1. ├── 01Givenratio = 100
  2. ├── 02FormuladB (power): 10 × log₁₀(t)
  3. ├── 03Compute dB (power)20
  4. ├── 04FormuladB (voltage): 20 × log₁₀(t)
  5. └── 05Compute dB (voltage)40
Did you know?

Exponent notation aⁿ was coined by Descartes in 1637 — three centuries after Indian and Arab mathematicians worked with the concept in words.

§01What is

Understanding the Power Ratio to dB

The Power Ratio to dB computes dB (power) from 1 input: ratio. 10 log₁₀(ratio).

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Power Ratio to dB sits in that toolkit — it 10 log₁₀(ratio). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

dB (power) = 10 × log₁₀(t) | dB (voltage) = 20 × log₁₀(t)

Where

ratio
Ratio
dB (power)
Output value
dB (voltage)
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Ratio = 100.

  1. 01Start by noting the input — Ratio: 100.
  2. 02Substitute these values into the formula: dB (power) = 10 × log₁₀(t) | dB (voltage) = 20 × log₁₀(t)
  3. 03Compute dB (power): the calculator returns 20.
  4. 04Compute dB (voltage): the calculator returns 40.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Power Ratio to dB Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Ratio halved

ratio = 50 (from 100)

Keep every other input at its default and halve the ratio. See how db (power) responds.

  1. 01New Ratio: 50
  2. 02Baseline dB (power): 20
  3. 03New dB (power): 16.9897
  4. 04dB (power) decreases by 15.1% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Ratio doubled

ratio = 200 (from 100)

Keep every other input at its default and double the ratio. See how db (power) responds.

  1. 01New Ratio: 200
  2. 02Baseline dB (power): 20
  3. 03New dB (power): 23.0103
  4. 04dB (power) increases by 15.1% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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