dBZ is radar reflectivity on a decibel scale: dBZ = 10·log10(Z), with Z in mm⁶/m³. 0 dBZ is Z = 1, and each 10 dBZ is ten times more reflectivity. NOAA’s scale runs from about −35 to +85 dBZ. Roughly 20–40 dBZ is light precipitation, 40–50 moderate and 50–65 heavy or some hail.

Which Z–R relation should I use?

Marshall–Palmer for general and stratiform rain, the NEXRAD default for summer convection and the tropical relation for warm, deep tropical rain. NOAA JetStream’s dBZ table matches Marshall–Palmer: 60 dBZ gives 205 mm/h there and here, 55 dBZ gives 100 there and 99.9 here, 50 dBZ 47 there and 48.6 here. That match is our own calculation, NOAA does not name the relation. The NWS radars use Z = 300·R^1.4 by default and switch to the tropical Z = 250·R^1.2 in tropical rain, where the default underestimates heavily.

Why do the relations give such different rain rates?

Because reflectivity and rain rate weigh drops differently. Z grows with the sixth power of the drop diameter, rain rate only with about the third to fourth power. A few large drops raise Z a lot without much water, and many small drops do the opposite. At 50 dBZ the three relations give 48.6, 63.4 and 147 mm/h. Which one is right depends on the drop sizes, and a single reflectivity value cannot tell them apart.

What is the NEXRAD 53 dBZ hail cap?

A ceiling on the estimated rain rate. The NEXRAD default stops at 103.8 mm/h (about 4 in/h), the rate Z = 300·R^1.4 gives at 53 dBZ, because stronger echoes are likely hail. With the tropical relation the same 103.8 mm/h corresponds to only about 48 dBZ, which is why the NWS study raised the cap for tropical events. This tool flags the cap but never clips the result.

Does this work for snow or hail?

No. These relations are for rain. Snow reflects less than rain with the same water content, while hail and melting snow reflect far more, so a rain relation gives misleading numbers for them. A snow relation is not offered because we could not check one against a primary source.

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Weather radar dBZ to rain rate converter

dBZ is weather radar reflectivity on a decibel scale, and a Z–R relation turns it into a rain rate. With the common Marshall–Palmer relation Z = 200·R^1.6, 40 dBZ is about 11.5 mm/h and 50 dBZ about 49 mm/h. This converter works both ways, with the NEXRAD default, the tropical relation or your own constants.

Direction

Reflectivity

As a radar map shows it, usually in dBZ. Switch to mm⁶/m³ for the linear factor Z.

Z–R relation

Marshall–Palmer is the classic choice and matches NOAA’s dBZ table. NEXRAD uses 300·R^1.4 by default.

Rain rate

11.5

relation: Marshall–Palmer

Reflectivity factor Z

10000 mm⁶/m³

= 40.0 dBZ

NWS intensity

Moderate

precipitation · 40 to 50 dBZ

Rain in 10 minutes

1.92

in one hour: 11.5 mm

Same echo with the other relations: NEXRAD 12.2 mm/h, tropical 21.6 mm/h.
40.0 dBZ sits exactly on an edge of the NWS scale. This tool counts an edge value in the higher band.

Rain rate against reflectivity for the three standard relations. The horizontal axis is reflectivity in dBZ, linear. The vertical axis is rain rate on a logarithmic scale, one decade per gridline, in the rain-rate unit you picked last. The relation you selected is drawn in green, the other two in grey (solid Marshall–Palmer, dashed NEXRAD, dotted tropical). The dot is your value. The amber line is the NEXRAD hail cap at 53 dBZ. The bands along the bottom are the NWS intensity scale.

A Z–R relation is an average over many storms. A single radar pixel can be off by a factor of two or more because of the drop sizes, hail, the melting layer, beam blockage or the beam overshooting low rain far from the radar. The NWS intensity names come from NOAA JetStream, which marks light and moderate with a caveat.

How it works

01
Read the reflectivity

A weather radar reports reflectivity in dBZ. Turn it into the reflectivity factor with Z = 10^dBZ/10, in mm⁶/m³. 40 dBZ is Z = 10 000, and every 10 dBZ is ten times more.
02
Pick a Z–R relation

Rain rate follows from a power law Z = a·R^b. Marshall–Palmer uses a = 200 and b = 1.6. The NEXRAD default uses 300 and 1.4, and the tropical relation 250 and 1.2. The constants describe a typical drop-size distribution, so pick the one that fits the weather.
03
Solve for the rain rate

R = (Z/a)^1/b in mm/h. The other way round, dBZ = 10·log₁₀(a) + 10·b·log₁₀(R). Because b is above 1, each 10 dBZ multiplies the rain rate by 10^1/b, about 4.2 for Marshall–Palmer.
04
Name the intensity

NOAA’s guidelines name the band: 20–40 dBZ light, 40–50 moderate, 50–65 heavy or some hail, above 65 extremely heavy with hail. A value exactly on an edge counts in the higher band here.

Formulas

Reflectivity in dBZ

dBZ = 10 · log₁₀(Z)

Z — reflectivity factor, mm⁶/m³
dBZ — Z on a decibel scale, 0 dBZ = 1 mm⁶/m³

Z–R relation and rain rate

Z = a · R^b, R = (Z / a)^1/b

R — rain rate, mm/h
a, b — constants: Marshall–Palmer 200 and 1.6, NEXRAD default 300 and 1.4, tropical 250 and 1.2

Rain rate → dBZ

dBZ = 10 · log₁₀(a) + 10 · b · log₁₀(R)

in/h = mm/h ÷ 25.4
rain in t hours = R · t, mm

Worked example

40 dBZ with Marshall–Palmer (the defaults)

Z = 10^40/10 = 10 000 mm⁶/m³
R = (10 000 / 200)^1/1.6 = 50^0.625 = 11.5 mm/h (0.454 in/h)
same echo, NEXRAD default 300·R^1.4: 12.2 mm/h, tropical 250·R^1.2: 21.6 mm/h
10 minutes at 11.5 mm/h: 11.5 / 6 = 1.92 mm of rain
→ 40 dBZ is the light/moderate edge of the NWS scale and counts as moderate

FAQ

What does dBZ mean?: dBZ is radar reflectivity on a decibel scale: dBZ = 10·log₁₀(Z), with Z in mm⁶/m³. 0 dBZ is Z = 1, and each 10 dBZ is ten times more reflectivity. NOAA’s scale runs from about −35 to +85 dBZ. Roughly 20–40 dBZ is light precipitation, 40–50 moderate and 50–65 heavy or some hail.
Which Z–R relation should I use?: Marshall–Palmer for general and stratiform rain, the NEXRAD default for summer convection and the tropical relation for warm, deep tropical rain. NOAA JetStream’s dBZ table matches Marshall–Palmer: 60 dBZ gives 205 mm/h there and here, 55 dBZ gives 100 there and 99.9 here, 50 dBZ 47 there and 48.6 here. That match is our own calculation, NOAA does not name the relation. The NWS radars use Z = 300·R^1.4 by default and switch to the tropical Z = 250·R^1.2 in tropical rain, where the default underestimates heavily.
Why do the relations give such different rain rates?: Because reflectivity and rain rate weigh drops differently. Z grows with the sixth power of the drop diameter, rain rate only with about the third to fourth power. A few large drops raise Z a lot without much water, and many small drops do the opposite. At 50 dBZ the three relations give 48.6, 63.4 and 147 mm/h. Which one is right depends on the drop sizes, and a single reflectivity value cannot tell them apart.
What is the NEXRAD 53 dBZ hail cap?: A ceiling on the estimated rain rate. The NEXRAD default stops at 103.8 mm/h (about 4 in/h), the rate Z = 300·R^1.4 gives at 53 dBZ, because stronger echoes are likely hail. With the tropical relation the same 103.8 mm/h corresponds to only about 48 dBZ, which is why the NWS study raised the cap for tropical events. This tool flags the cap but never clips the result.
Does this work for snow or hail?: No. These relations are for rain. Snow reflects less than rain with the same water content, while hail and melting snow reflect far more, so a rain relation gives misleading numbers for them. A snow relation is not offered because we could not check one against a primary source.

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Sources & further reading

Radar Images: Reflectivity — NOAA JetStream ↗ — the dBZ scale, the intensity guidelines and the dBZ to rain-rate table
An Investigation of Rainfall Estimates Generated by the WSR-88D PPS Algorithm under Various Parameterizations of the ‘Z-R’ Relationship and ‘Hail Cap’ Threshold, chapter 2 — NWS Office of Hydrologic Development ↗ — NEXRAD default Z = 300·R^1.4, tropical Z = 250·R^1.2, hail cap 103.8 mm/h at 53 dBZ
Next Generation Weather Radar (NEXRAD) — NOAA NCEI ↗ — the network of 160 S-band WSR-88D radars and its documentation
J. S. Marshall and W. McK. Palmer, “The distribution of raindrops with size”, Journal of Meteorology 5 (1948), 165–166 — origin of the Marshall–Palmer relation, conventionally written Z = 200·R^1.6
D. Rosenfeld, D. B. Wolff and D. Atlas, “General probability-matched relations between radar reflectivity and rain rate”, Journal of Applied Meteorology 32 (1993), 50–72 — the tropical relation Z = 250·R^1.2
DBZ (meteorology) — Wikipedia ↗ — background on the unit, read 7 November 2026

Weather radar dBZ to rain rate converter

How it works

Read the reflectivity

Pick a Z–R relation

Solve for the rain rate

Name the intensity

Formulas

Worked example

FAQ

Related guides

Sources & further reading

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