{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"decibel"},"result":{"entity_type":"calculator","id":"decibel","calculator_id":"decibel","canonical_url":"https://tttkmbb.com/engineering/decibel","name":"Decibel Calculator","title":"Decibel Calculator – Power and Amplitude Ratios to dB and Back, dBm to mW","category":"engineering","category_name":"Engineering & Automotive","tool_name":"convert_decibels","featured_mcp_tool":false,"description":"Converts between a linear ratio and decibels using 10·log10 for power quantities or 20·log10 for amplitude quantities (voltage, current, sound pressure), and between dBm and milliwatts (0 dBm = 1 mW).","use_when":"You need to express a gain, loss or signal ratio in dB, turn a dB figure back into a ratio, or convert an RF power level between dBm and mW/W.","do_not_use_when":"You need to add two sound levels or account for distance attenuation, or you need plain logarithms (use logarithm).","inputs":[{"name":"quantity","label":"Quantity type","type":"enum","required":false,"default":"power","values":[{"value":"power","label":"Power ratio (10·log10)","aliases":["watts","energy","intensity"]},{"value":"amplitude","label":"Amplitude ratio: voltage, current, sound pressure (20·log10)","aliases":["voltage","current","field","pressure"]},{"value":"dbm","label":"dBm ↔ milliwatts (absolute power, 0 dBm = 1 mW)"}],"description":"Whether the linear value is a power ratio, an amplitude (field) ratio, or an absolute power in mW for dBm.","example":"power"},{"name":"linear_value","label":"Linear value","type":"number","required":false,"exclusive_min":0,"description":"The ratio (output/input), or the power in milliwatts for quantity=dbm. Give either linear_value or decibel_value.","example":1000},{"name":"decibel_value","label":"Decibel value","type":"number","unit":"dB","required":false,"description":"Level in dB (or dBm for quantity=dbm). Give either linear_value or decibel_value."}],"outputs":[{"name":"solved_for","label":"Solved for","type":"string","decimals":4,"description":"decibel_value or linear_value."},{"name":"decibel_value","label":"Decibels","type":"number","unit":"dB","decimals":4,"description":"10·log10(ratio) for power, 20·log10(ratio) for amplitude, 10·log10(mW) for dBm."},{"name":"linear_value","label":"Linear value","type":"number","decimals":6,"description":"The ratio, or milliwatts for dBm."},{"name":"power_ratio","label":"Equivalent power ratio","type":"number","decimals":6,"description":"10^(dB/10): the power ratio corresponding to this dB value."},{"name":"amplitude_ratio","label":"Equivalent amplitude ratio","type":"number","decimals":6,"description":"10^(dB/20): the voltage/current ratio corresponding to this dB value (power and amplitude modes)."},{"name":"milliwatts","label":"Power","type":"number","unit":"mW","decimals":6,"description":"Absolute power (dBm mode only)."},{"name":"watts","label":"Power","type":"number","unit":"W","decimals":9,"description":"Absolute power in watts (dBm mode only)."},{"name":"dbw","label":"Level","type":"number","unit":"dBW","decimals":4,"description":"dBm − 30 (dBm mode only)."},{"name":"interpretation","label":"Interpretation","type":"string","decimals":4,"description":"Plain-language reading of the result."}],"input_schema":{"type":"object","properties":{"quantity":{"description":"Whether the linear value is a power ratio, an amplitude (field) ratio, or an absolute power in mW for dBm.","type":"string","enum":["power","amplitude","dbm"],"default":"power","examples":["power"]},"linear_value":{"description":"The ratio (output/input), or the power in milliwatts for quantity=dbm. Give either linear_value or decibel_value.","type":"number","exclusiveMinimum":0,"examples":[1000]},"decibel_value":{"description":"Level in dB (or dBm for quantity=dbm). Give either linear_value or decibel_value. Unit: dB.","type":"number","x-unit":"dB"}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"solved_for":{"description":"decibel_value or linear_value.","type":"string"},"decibel_value":{"description":"10·log10(ratio) for power, 20·log10(ratio) for amplitude, 10·log10(mW) for dBm. Unit: dB.","type":"number","x-unit":"dB"},"linear_value":{"description":"The ratio, or milliwatts for dBm.","type":"number"},"power_ratio":{"description":"10^(dB/10): the power ratio corresponding to this dB value.","type":"number"},"amplitude_ratio":{"description":"10^(dB/20): the voltage/current ratio corresponding to this dB value (power and amplitude modes).","type":"number"},"milliwatts":{"description":"Absolute power (dBm mode only). Unit: mW.","type":"number","x-unit":"mW"},"watts":{"description":"Absolute power in watts (dBm mode only). Unit: W.","type":"number","x-unit":"W"},"dbw":{"description":"dBm − 30 (dBm mode only). Unit: dBW.","type":"number","x-unit":"dBW"},"interpretation":{"description":"Plain-language reading of the result.","type":"string"}}},"formula":"power: dB = 10 × log10(ratio), ratio = 10^(dB/10); amplitude: dB = 20 × log10(ratio), ratio = 10^(dB/20); dBm = 10 × log10(P_mW), P_mW = 10^(dBm/10); dBW = dBm − 30","method":"Amplitude quantities use 20·log10 because power is proportional to amplitude squared, so both conventions give the same dB for the same physical change. A negative dB value means attenuation (ratio below 1).","sources":[{"name":"Wikipedia – Decibel","url":"https://en.wikipedia.org/wiki/Decibel","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – dBm","url":"https://en.wikipedia.org/wiki/DBm","type":"reference","retrieved_at":"2026-09-24"},{"name":"NIST Special Publication 811 – Guide for the Use of the SI, Appendix B (conversion factors)","url":"https://www.nist.gov/pml/special-publication-811","type":"standard","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Power ratio 1000","inputs":{"quantity":"power","linear_value":1000},"expected":{"solved_for":"decibel_value","decibel_value":30,"power_ratio":1000,"amplitude_ratio":31.622777,"interpretation":"Gain of 30 dB: output power is 1000× the input"},"url":"https://tttkmbb.com/api/v1/calculate/decibel?quantity=power&linear_value=1000"},{"name":"20 dBm to milliwatts","inputs":{"quantity":"dbm","decibel_value":20},"expected":{"solved_for":"linear_value","linear_value":100,"milliwatts":100,"watts":0.1,"dbw":-10},"url":"https://tttkmbb.com/api/v1/calculate/decibel?quantity=dbm&decibel_value=20"}],"faq":[{"q":"Is doubling 3 dB or 6 dB?","a":"Doubling the power is +3.01 dB; doubling the voltage (or current or sound pressure) is +6.02 dB, which is also a 4× power increase."},{"q":"What is the difference between dB and dBm?","a":"dB is a ratio with no unit; dBm is an absolute power referenced to 1 mW (0 dBm = 1 mW, 30 dBm = 1 W, −30 dBm = 1 µW)."}],"tags":["decibel","db calculator","dbm to mw","power ratio to db","voltage gain db","20 log"],"related":[{"calculator_id":"logarithm","reason":"The underlying base-10 logarithm."},{"calculator_id":"electric-power","reason":"Absolute electrical power from voltage and current."},{"calculator_id":"exponent","reason":"Evaluate 10^(dB/10) directly."}],"links":{"html":"https://tttkmbb.com/engineering/decibel","markdown":"https://tttkmbb.com/engineering/decibel.md","json":"https://tttkmbb.com/engineering/decibel.json","api":"https://tttkmbb.com/api/v1/calculate/decibel","schema":"https://tttkmbb.com/api/v1/calculators/decibel","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T01:51:01Z"}