Choose the number of bands on the resistor and the color of each band, then press "Calculate". Each option is shown as "color (value)".
When you change the number of bands, only the fields you need are shown (the 3rd digit for 5 and 6 bands, tolerance for 4 bands or more, and temperature coefficient for 6 bands). A 3-band resistor is treated as ±20% tolerance.
Result and figure
Choose the number of bands and the color of each band on the left, then press "Calculate". The resistance and a drawing of the resistor with its color bands will appear here.
Table of Contents
-
What you can do on this page
-
What is this calculation used for?
-
How to Use
-
Formulas and figures
-
Symbols and terms
-
Good to know before you start
-
How to calculate it in Excel
-
How to calculate it in Google Sheets
-
How to calculate it in Python
-
How to write it in LaTeX and other math languages (copy and paste)
-
How to have ChatGPT do the calculation
-
DataChef Features
-
Related Features
-
NumberChef Calculators List
What you can do on this page
- Just choose the colors of a resistor's bands (the color code) to read its resistance (Ω). Works for 3, 4, 5 and 6 bands
- You also get the tolerance (±% and letter codes such as F and J) and the actual resistance range (minimum to maximum) that the tolerance allows
- For 6-band resistors, the temperature coefficient (ppm/K) is read too
- A drawing of the resistor with the colors you chose appears on the spot (you can save it as PNG or SVG)
- A plain-language explanation of the formulas, a color-to-number chart and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The colors and values follow the standard chart of the international standard IEC 60062. A 3-band resistor has no tolerance band, so its tolerance is treated as ±20% (code M).
What is this calculation used for?
Choosing resistors for electronics projects (Arduino, Raspberry Pi, LEDs)
When you connect an LED to a power supply, you need a resistor to limit the current. For example, to run 10 mA through an LED with a forward voltage of 2 V from a 5 V supply, you need \((5-2) \div 0.01 = 300\) Ω.
Every time you pick a 300 Ω resistor (orange, black, brown) out of a parts box, or check that the resistors you bought are the right value, you need to read the color code. It is the most-used basic skill in electronics projects.
Finding the value of a resistor on a circuit board when repairing electronics
For repairs and part replacements, you need a replacement with the same value as the resistor on the board. Resistors often have no numbers printed on them, so you read the value from the color bands.
For example, brown, black, orange, gold is 10 kΩ ±5%. If the value you measure with a multimeter falls within the tolerance range (9,500 Ω to 10,500 Ω here), that is a good sign the resistor is not damaged.
Note that devices that plug into a wall outlet contain parts (capacitors) that keep storing electricity even after unplugging, which can give an electric shock. Repairs that involve taking a device apart are for people with electrical knowledge. If you are not confident, leave it to a professional repair service.
Checking resistor values in school labs (technology, physics, electronics)
In school science labs (such as Ohm's law experiments), technology classes and electronics courses at technical schools and colleges, students pick the specified resistors themselves and build circuits.
A classic reason an experiment fails is using the wrong resistor. If both the people handing out parts and the people using them get in the habit of reading the color bands to check the value, there are fewer experiments to redo.
Checking parts against the design in manufacturing and inspection
In electronics manufacturing, workers check that the resistors being mounted have the value and tolerance on the bill of materials (BOM). For example, a precision measuring circuit may call for precision resistors of ±1% (brown) or better, and mixing them up with general ±5% (gold) parts hurts performance.
Tolerance letter codes (F = ±1%, J = ±5% and so on) also appear in part numbers, so knowing how the bands match the codes makes it easier to check the BOM against the actual parts.
Formulas and figures
Formula for the resistance of 3-band and 4-band resistors (2 digits)
Figure
Standard notation
(the usual math form)
\(R\)
\(=\)
\((\)
\(10 \times\)
\(d_1\)
\(+\)
\(d_2\)
\()\)
\(\times\)
\(m\)
In words
(symbols replaced with words)
④
\(R\): resistance
\(=\)
\((\)
\(10 \times\)
①
\(d_1\): 1st digit
\(+\)
②
\(d_2\): 2nd digit
\()\)
\(\times\)
③
\(m\): multiplier
The formula in words
①
Take the
\(d_1\): digit of the 1st band
and multiply it by 10
②
add the
\(d_2\): digit of the 2nd band
(this makes a 2-digit number)
③
multiply by the
\(m\): multiplier (the factor of the 3rd band)
④
and you get the
\(R\): resistance
(in Ω)
Quick example
The resistance of a 4-band resistor with bands brown (1), black (0), red (×100) in that order is
\(R\): resistance
\(=\)
\((\)
\(10 \times\)
brown (1)
\(+\)
black (0)
\()\)
\(\times\)
red (×100)
\((10 \times 1 + 0) \times 100 = 1000\ \Omega = 1\,\mathrm{k\Omega}\)
Key idea
The colors stand for these digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9 (the full chart is in "Symbols and terms" and in the Excel table).
You can think of the multiplier as "how many zeros to add". Red (×100) adds 2 zeros and orange (×1,000) adds 3. Gold (×0.1) and silver (×0.01) do the opposite and move the decimal point to the left.
The digits are read the same way on 3-band and 4-band resistors. The 4th band (gold, silver and so on) shows the tolerance and is not used to calculate the resistance itself.
Formula for the resistance of 5-band and 6-band resistors (3 digits)
Figure
Standard notation
(the usual math form)
\(R\)
\(=\)
\((\)
\(100 \times\)
\(d_1\)
\(+\)
\(10 \times\)
\(d_2\)
\(+\)
\(d_3\)
\()\)
\(\times\)
\(m\)
In words
(symbols replaced with words)
⑤
\(R\): resistance
\(=\)
\((\)
\(100 \times\)
①
\(d_1\): 1st digit
\(+\)
\(10 \times\)
②
\(d_2\): 2nd digit
\(+\)
③
\(d_3\): 3rd digit
\()\)
\(\times\)
④
\(m\): multiplier
The formula in words
①
Take the
\(d_1\): digit of the 1st band
and multiply it by 100
②
add the
\(d_2\): digit of the 2nd band
multiplied by 10
③
add the
\(d_3\): digit of the 3rd band
(this makes a 3-digit number)
④
multiply by the
\(m\): multiplier (the factor of the 4th band)
⑤
and you get the
\(R\): resistance
(in Ω)
Quick example
The resistance of a 5-band resistor with bands red (2), violet (7), black (0), orange (×1,000) in that order is
\(R\): resistance
\(=\)
\((\)
\(100 \times\)
red (2)
\(+\)
\(10 \times\)
violet (7)
\(+\)
black (0)
\()\)
\(\times\)
orange (×1,000)
\((100 \times 2 + 10 \times 7 + 0) \times 1000 = 270000\ \Omega = 270\,\mathrm{k\Omega}\)
Key idea
5-band and 6-band resistors have 3 digit bands, so they can show finer values such as 47.5 kΩ (they are called precision resistors).
The 6th band of a 6-band resistor shows the temperature coefficient (how easily the resistance changes with temperature). It is not used to calculate the resistance itself either.
Formula for the actual resistance range from the tolerance
Figure
Standard notation
(the usual math form)
\(R_{\mathrm{min}}\)
\(=\)
\(R\)
\(\times\)
\(\left( 1 - \dfrac{t}{100} \right)\)
\(R_{\mathrm{max}}\)
\(=\)
\(R\)
\(\times\)
\(\left( 1 + \dfrac{t}{100} \right)\)
In words
(symbols replaced with words)
③
minimum resistance
\(=\)
①
\(R\): resistance
\(\times\)
②
1 − tolerance rate
⑤
maximum resistance
\(=\)
\(R\): resistance
\(\times\)
④
1 + tolerance rate
The formula in words
①
Take the
\(R\): resistance read from the colors
②
multiply it by
1 − tolerance rate (the tolerance \(t\) % divided by 100)
③
to get the
minimum resistance \(R_{min}\)
④
and multiply it by
1 + tolerance rate
⑤
to get the
maximum resistance \(R_{max}\)
Quick example
The actual resistance range of a 1 kΩ (1,000 Ω) resistor with ±5% tolerance (gold) is
minimum resistance
\(=\)
resistance (1,000 Ω)
\(\times\)
1 − 0.05
maximum resistance
\(=\)
resistance (1,000 Ω)
\(\times\)
1 + 0.05
\(1000 \times (1 - 0.05) = 950\ \Omega\)
\(1000 \times (1 + 0.05) = 1050\ \Omega\)
Key idea
The tolerance is a guarantee that manufacturing variation stays within this range. A 1 kΩ resistor with ±5% (gold) is somewhere between 950 Ω and 1,050 Ω.
When a circuit needs an accurate resistance, choose a 5-band precision resistor with a small tolerance (such as ±1%, brown).
A resistor color code works like this - line up the digit bands from the left to make a 2-digit number (3 digits on precision resistors), then multiply by the factor of the multiplier color. The tolerance band shows the guaranteed limit on how far the real resistance can be from the marked value.
Symbols and terms
Symbols
| \(R\) | are | The resistance read from the colors (the marked value of the resistor). The unit is Ω (ohms). |
| \(d_1, d_2, d_3\) | d one, d two, d three | The digits (0 to 9) shown by the 1st, 2nd and 3rd bands. Only 5-band and 6-band resistors have the 3rd digit \(d_3\). |
| \(m\) | em | The multiplier, the factor you multiply the digits by. It ranges from ×0.01 (silver) to ×1,000,000,000 (white). |
| \(t\) | tee | The tolerance (%). For example, a gold band gives \(t = 5\) (±5%). |
| \(R_{min}\), \(R_{max}\) | R min, R max | The minimum and maximum of the real resistance, allowing for the tolerance. The real resistor is somewhere in this range. |
| \(\Omega\) | ohm | The unit of resistance. 1,000 Ω = 1 kΩ (kilohm) and 1,000,000 Ω = 1 MΩ (megohm). |
| ppm/K | parts per million per kelvin | The unit of the temperature coefficient: how many millionths the resistance changes when the temperature changes by 1 K (the same size as 1 °C). For example, if a 1 kΩ, 50 ppm/K resistor warms up by 10 °C (18 °F), it changes by at most 1,000 × 50 ÷ 1,000,000 × 10 = 0.5 Ω. |
Terms
| resistance | How strongly something resists the flow of current. At the same voltage, the higher the resistance, the smaller the current. Its relation to voltage \(V\) (V) and current \(I\) (A) is Ohm's law, \(R = \dfrac{V}{I}\), and its unit is Ω (ohms). |
| nominal value | The resistance marked on a resistor (for example, 4.7 kΩ). This is the value this page reads from the color code. The real resistance can differ from the nominal value by up to the tolerance, so it falls somewhere between \(R_{min}\) and \(R_{max}\). |
| color code | An international system that shows the value of resistors and other parts with colored bands. The digits are black = 0, brown = 1, red = 2, orange = 3, yellow = 4, green = 5, blue = 6, violet = 7, gray = 8, white = 9. The same color means a digit, a multiplier or a tolerance depending on its position. |
| resistor | An electronic part that resists current. It is used to set the current in a circuit and to divide voltage. Resistors are too small to print numbers on easily, so their values are shown with color bands. |
| multiplier | The band that gives the factor to multiply the digits by. It grows 10 times at each step in the same order as the digits: black = ×1, brown = ×10, red = ×100 and so on (white = ×1 billion). Gold = ×0.1 and silver = ×0.01 are used for small resistances, from under 1 Ω to a few Ω. |
| tolerance | The guaranteed limit on how far the real resistance may be from the marked value (±%). Brown = ±1%, red = ±2%, green = ±0.5%, blue = ±0.25%, violet = ±0.1%, gray = ±0.01%, orange = ±0.05%, yellow = ±0.02%, gold = ±5%, silver = ±10%. It is also shown with letter codes such as F (±1%), J (±5%), K (±10%) and M (±20%). |
| temperature coefficient | How easily the resistance changes when the temperature changes (ppm/K), also called TCR. It is the 6th band of a 6-band resistor: black = 250, brown = 100, red = 50, orange = 15, yellow = 25, green = 20, blue = 10, violet = 5, gray = 1 ppm/K. It matters in circuits that must stay accurate as the temperature changes, such as measuring circuits. |
| E series | The series of standard values that resistors are sold in (IEC 60063). For example, the E12 series is the 12 values 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8 and 8.2, repeated at every power of 10, and the resistors sold in stores have one of these values. If the value you read is not in the E series (for example, the 1st band is black), you may be reading the bands backward. |
| IEC 60062 | The international standard that sets how the values of resistors and capacitors are marked (color codes and letter codes). The color chart on this page is based on this standard. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Place value and large numbers (Grade 4) |
|
| Decimals and percents (Grade 6) |
|
| Powers of 10 and unit prefixes (Grades 6–8 math and science) |
|
| Ohm's law (middle and high school science) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Color chart (digit, multiplier, tolerance, temperature coefficient)
| Color | Digit | Multiplier | Tolerance (±%) | Temp. coefficient (ppm/K) |
| Black | 0 | 1 | 250 | |
| Brown | 1 | 10 | 1 | 100 |
| Red | 2 | 100 | 2 | 50 |
| Orange | 3 | 1000 | 0.05 | 15 |
| Yellow | 4 | 10000 | 0.02 | 25 |
| Green | 5 | 100000 | 0.5 | 20 |
| Blue | 6 | 1000000 | 0.25 | 10 |
| Violet | 7 | 10000000 | 0.1 | 5 |
| Gray | 8 | 100000000 | 0.01 | 1 |
| White | 9 | 1000000000 | ||
| Gold | 0.1 | 5 | ||
| Silver | 0.01 | 10 |
Table to find the resistance and range of a 4-band resistor (example - brown, black, red, gold)
| 1st digit (brown = 1) | 1 |
| 2nd digit (black = 0) | 0 |
| Multiplier (red = 100) | 100 |
| Tolerance % (gold = 5) | 5 |
| Resistance (Ω) | =(B1*10+B2)*B3 |
| Minimum resistance (Ω) | =B5*(1-B4/100) |
| Maximum resistance (Ω) | =B5*(1+B4/100) |
Table to find the resistance and range of a 5-band resistor (example - red, violet, black, orange, brown)
| 1st digit (red = 2) | 2 |
| 2nd digit (violet = 7) | 7 |
| 3rd digit (black = 0) | 0 |
| Multiplier (orange = 1000) | 1000 |
| Tolerance % (brown = 1) | 1 |
| Resistance (Ω) | =(B1*100+B2*10+B3)*B4 |
| Minimum resistance (Ω) | =B6*(1-B5/100) |
| Maximum resistance (Ω) | =B6*(1+B5/100) |
The first table is the color chart (quick reference). Use it to turn the colors on your resistor into numbers.
The second table is for 4 bands. Enter the numbers you read from the colors in B1 to B4, and B5 gives the resistance while B6 and B7 give the range with tolerance. "*" is multiplication and "/" is division.
With the example values (brown, black, red, gold), B5 shows 1000 (= 1 kΩ), B6 shows 950 and B7 shows 1050.
The third table is for 5 bands; the formula changes only because there are 3 digits. With the example values (red, violet, black, orange, brown), B6 shows 270000 (= 270 kΩ).
The second table is for 4 bands. Enter the numbers you read from the colors in B1 to B4, and B5 gives the resistance while B6 and B7 give the range with tolerance. "*" is multiplication and "/" is division.
With the example values (brown, black, red, gold), B5 shows 1000 (= 1 kΩ), B6 shows 950 and B7 shows 1050.
The third table is for 5 bands; the formula changes only because there are 3 digits. With the example values (red, violet, black, orange, brown), B6 shows 270000 (= 270 kΩ).
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Color chart (digit, multiplier, tolerance, temperature coefficient)
| Color | Digit | Multiplier | Tolerance (±%) | Temp. coefficient (ppm/K) |
| Black | 0 | 1 | 250 | |
| Brown | 1 | 10 | 1 | 100 |
| Red | 2 | 100 | 2 | 50 |
| Orange | 3 | 1000 | 0.05 | 15 |
| Yellow | 4 | 10000 | 0.02 | 25 |
| Green | 5 | 100000 | 0.5 | 20 |
| Blue | 6 | 1000000 | 0.25 | 10 |
| Violet | 7 | 10000000 | 0.1 | 5 |
| Gray | 8 | 100000000 | 0.01 | 1 |
| White | 9 | 1000000000 | ||
| Gold | 0.1 | 5 | ||
| Silver | 0.01 | 10 |
Table to find the resistance and range of a 4-band resistor (example - brown, black, red, gold)
| 1st digit (brown = 1) | 1 |
| 2nd digit (black = 0) | 0 |
| Multiplier (red = 100) | 100 |
| Tolerance % (gold = 5) | 5 |
| Resistance (Ω) | =(B1*10+B2)*B3 |
| Minimum resistance (Ω) | =B5*(1-B4/100) |
| Maximum resistance (Ω) | =B5*(1+B4/100) |
Table to find the resistance and range of a 5-band resistor (example - red, violet, black, orange, brown)
| 1st digit (red = 2) | 2 |
| 2nd digit (violet = 7) | 7 |
| 3rd digit (black = 0) | 0 |
| Multiplier (orange = 1000) | 1000 |
| Tolerance % (brown = 1) | 1 |
| Resistance (Ω) | =(B1*100+B2*10+B3)*B4 |
| Minimum resistance (Ω) | =B6*(1-B5/100) |
| Maximum resistance (Ω) | =B6*(1+B5/100) |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and change the numbers in column B to match the colors of your resistor.
How to calculate it in Python
# Color chart (IEC 60062)
digit_of_color = {'black': 0, 'brown': 1, 'red': 2, 'orange': 3, 'yellow': 4,
'green': 5, 'blue': 6, 'violet': 7, 'gray': 8, 'white': 9}
multiplier_of_color = {'black': 1, 'brown': 10, 'red': 100, 'orange': 1000, 'yellow': 10000,
'green': 100000, 'blue': 1000000, 'violet': 10000000,
'gray': 100000000, 'white': 1000000000, 'gold': 0.1, 'silver': 0.01}
tolerance_of_color = {'brown': 1, 'red': 2, 'orange': 0.05, 'yellow': 0.02, 'green': 0.5,
'blue': 0.25, 'violet': 0.1, 'gray': 0.01, 'gold': 5, 'silver': 10}
band1 = 'brown' # color of the 1st band (1st digit)
band2 = 'black' # color of the 2nd band (2nd digit)
multiplier = 'red' # color of the multiplier band
tolerance = 'gold' # color of the tolerance band
resistance = (digit_of_color[band1] * 10 + digit_of_color[band2]) * multiplier_of_color[multiplier]
tolerance_percent = tolerance_of_color[tolerance]
resistance_min = resistance * (1 - tolerance_percent / 100)
resistance_max = resistance * (1 + tolerance_percent / 100)
print(f"Resistance: {resistance} Ω")
print(f"Tolerance: ±{tolerance_percent}%")
print(f"Actual resistance range: {resistance_min} Ω to {resistance_max} Ω")
Runs with the standard library only. It first turns the colors into numbers with the chart at the top, then calculates. For a 5-band resistor, change the resistance line to "(1st digit × 100 + 2nd digit × 10 + 3rd digit) × multiplier".
How to write it in LaTeX and other math languages (copy and paste)
Formula for the resistance of 3-band and 4-band resistors (2 digits)
R = (10 × d₁ + d₂) × m
R = (10 d_{1} + d_{2}) \times m
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi>
<mo>=</mo>
<mo>(</mo>
<mn>10</mn>
<mo>×</mo>
<msub><mi>d</mi><mn>1</mn></msub>
<mo>+</mo>
<msub><mi>d</mi><mn>2</mn></msub>
<mo>)</mo>
<mo>×</mo>
<mi>m</mi>
</mrow>
</math>
R = (10 d_1 + d_2) xx m
(10 d1 + d2) m
R := (10*d1 + d2)*m;
R = (10*d1 + d2)*m;
R = (10 d_1 + d_2) × m
Formula for the resistance of 5-band and 6-band resistors (3 digits)
R = (100 × d₁ + 10 × d₂ + d₃) × m
R = (100 d_{1} + 10 d_{2} + d_{3}) \times m
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi>
<mo>=</mo>
<mo>(</mo>
<mn>100</mn>
<mo>×</mo>
<msub><mi>d</mi><mn>1</mn></msub>
<mo>+</mo>
<mn>10</mn>
<mo>×</mo>
<msub><mi>d</mi><mn>2</mn></msub>
<mo>+</mo>
<msub><mi>d</mi><mn>3</mn></msub>
<mo>)</mo>
<mo>×</mo>
<mi>m</mi>
</mrow>
</math>
R = (100 d_1 + 10 d_2 + d_3) xx m
(100 d1 + 10 d2 + d3) m
R := (100*d1 + 10*d2 + d3)*m;
R = (100*d1 + 10*d2 + d3)*m;
R = (100 d_1 + 10 d_2 + d_3) × m
Formula for the actual resistance range from the tolerance
Rmin = R × (1 − t/100), Rmax = R × (1 + t/100)
R_{\min} = R \left( 1 - \frac{t}{100} \right), \quad R_{\max} = R \left( 1 + \frac{t}{100} \right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub><mi>R</mi><mi>min</mi></msub>
<mo>=</mo>
<mi>R</mi>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>−</mo>
<mfrac><mi>t</mi><mn>100</mn></mfrac>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msub><mi>R</mi><mi>max</mi></msub>
<mo>=</mo>
<mi>R</mi>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>+</mo>
<mfrac><mi>t</mi><mn>100</mn></mfrac>
<mo>)</mo>
</mrow>
</mrow>
</math>
R_(min) = R xx (1 - t/100), R_(max) = R xx (1 + t/100)
{R (1 - t/100), R (1 + t/100)}
Rmin := R*(1 - t/100); Rmax := R*(1 + t/100);
Rmin = R*(1 - t/100); Rmax = R*(1 + t/100);
R_min = R(1 - t/100), R_max = R(1 + t/100)
How to have ChatGPT do the calculation
You are a calculation assistant for electronic components. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). Read a resistor color code. Use the IEC 60062 standard chart (black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, gray 8, white 9; multipliers ×1 to ×1 billion in the same order, gold = ×0.1, silver = ×0.01; tolerance gold = ±5%, silver = ±10%, brown = ±1%). A 4-band resistor has the bands brown, black, red, gold, in order from one end. Find each of the following: 1. The resistance (in Ω, and in easy-to-read kΩ) 2. The tolerance (±%) 3. The actual resistance range allowing for the tolerance (minimum to maximum) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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