Decibel Calculator
A power ratio of 100 is 20 dB; the same factor in voltage would be 40 dB, because power goes with voltage squared.
20 dB
- Rule of thumb
- +3 dB ≈ ×2 power, +10 dB = ×10 power, +6 dB ≈ ×2 voltage, +20 dB = ×10 voltage
Step-by-step solution
- dB = 10 log₁₀(100)
- = 20 dB
Decibel Formula
dB = 10 log₁₀(P₂/P₁) = 20 log₁₀(V₂/V₁)
dBm = 10 log₁₀(P / 1 mW)
Worked Example
A power ratio of 100:
- dB = 10 log₁₀(100)
- = 20 dB
GATE tip
Cascaded gains in dB simply add: a 20 dB amplifier, a −6 dB cable and a 10 dB amplifier give 24 dB overall. Convert to dB first, add, then convert back if needed.
More Analog and Digital Electronics Calculators
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Inverting −R_f/Rᵢₙ, non-inverting 1 + R_f/Rᵢₙ
difference (R_f/Rᵢₙ)(V₂ − V₁); in-amp 1 + 2R/R_G; summing −(R_f/Rᵢₙ)ΣV
Example: An inverting amplifier with Rᵢₙ = 10 kΩ, R_f = 100 kΩ and 0.2 V in: Voltage gain = -10.
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ADC Resolution Calculator
LSB = Vref / 2ⁿ, SNR = 6.02n + 1.76 dB
code = floor(Vᵢₙ/LSB); ENOB = (SINAD − 1.76)/6.02
Example: A 12-bit ADC with a 3.3 V reference converting 1.65 V: Resolution (1 LSB) = 0.805664 mV.
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555 Timer Calculator
f = 1/(ln 2 (R₁ + 2R₂)C) ≈ 1.44/((R₁ + 2R₂)C)
duty = (R₁ + R₂)/(R₁ + 2R₂); monostable T = ln 3 × RC ≈ 1.1RC
Example: An astable 555 with R₁ = 1 kΩ, R₂ = 10 kΩ and C = 10 µF: Frequency f = 6.86998 Hz.
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R = (V_s − n V_f) / I_f
n LEDs in series; resistor power P = (V_s − nV_f) I_f
Example: One 2 V LED at 20 mA from a 5 V supply: Series resistor R = 150 Ω.
Frequently asked questions
Why 10 log for power but 20 log for voltage?
Power ∝ V², and log(V²) = 2 log V. Both give the same dB for the same change when the impedance is the same.
What is dBm?
Power relative to 1 mW: 0 dBm = 1 mW, 30 dBm = 1 W, −30 dBm = 1 µW. Radio and fibre links budget in dBm.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Decibel Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/decibel-calculator/
IEEE
Scientific Converters, "Decibel Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/decibel-calculator/