How to Do a Linear Calibration Curve in Excel (2022)

How to Do a Linear Calibration Curve in Excel (1)

Excel has built-in features that you can use to display your calibration data and calculate a line-of-best-fit. This can be helpful when you are writing a chemistry lab report or programming a correction factor into a piece of equipment.

In this article, we’ll look at how to use Excel to create a chart, plot a linear calibration curve, display the calibration curve’s formula, and then set up simple formulas with the SLOPE and INTERCEPT functions to use the calibration equation in Excel.

What is a Calibration Curve and How is Excel Useful When Creating One?

To perform a calibration, you compare the readings of a device (like the temperature that a thermometer displays) to known values called standards (like the freezing and boiling points of water). This lets you create a series of data pairs that you’ll then use to develop a calibration curve.

A two-point calibration of a thermometer using the freezing and boiling points of water would have two data pairs: one from when the thermometer is placed in ice water (32°F or 0°C) and one in boiling water (212°F or 100°C). When you plot those two data pairs as points and draw a line between them (the calibration curve), then assuming the response of the thermometer is linear, you could pick any point on the line that corresponds to the value the thermometer displays, and you could find the corresponding “true” temperature.

So, the line is essentially filling in the information between the two known points for you so that you can be reasonably certain when estimating the actual temperature when the thermometer is reading 57.2 degrees, but when you have never measured a “standard” that corresponds to that reading.

Excel has features that allow you to plot the data pairs graphically in a chart, add a trendline (calibration curve), and display the calibration curve’s equation on the chart. This is useful for a visual display, but you can also calculate the formula of the line using Excel’s SLOPE and INTERCEPT functions. When you enter these values into simple formulas, you will be able to automatically calculate the “true” value based on any measurement.

Let’s Look at an Example

For this example, we will develop a calibration curve from a series of ten data pairs, each consisting of an X-value and a Y-value. The X-values will be our “standards,” and they could represent anything from the concentration of a chemical solution we are measuring using a scientific instrument to the input variable of a program that controls a marble launching machine.

The Y-values will be the “responses,” and they would represent the reading the instrument provided when measuring each chemical solution or the measured distance of how far away from the launcher the marble landed using each input value.

After we graphically depict the calibration curve, we will use the SLOPE and INTERCEPT functions to calculate the calibration line’s formula and determine the concentration of an “unknown” chemical solution based on the instrument’s reading or decide what input we should give the program so that the marble lands a certain distance away from the launcher.

Step One: Create Your Chart

Our simple example spreadsheet consists of two columns: X-Value and Y-Value.

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Let’s start by selecting the data to plot in the chart.

First, select the ‘X-Value’ column cells.

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Now press the Ctrl key and then click the Y-Value column cells.

How to Do a Linear Calibration Curve in Excel (4)

Go to the “Insert” tab.

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Navigate to the “Charts” menu and select the first option in the “Scatter” drop-down.

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A chart will appear containing the data points from the two columns.

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(Video) Using Excel for a Calibration Curve

Select the series by clicking on one of the blue points. Once selected, Excel outlines the points will be outlined.

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Right-click one of the points and then select the “Add Trendline” option.

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A straight line will appear on the chart.

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On the right side of the screen, the “Format Trendline” menu will appear. Check the boxes next to “Display Equation on chart” and “Display R-squared value on chart.” The R-squared value is a statistic that tells you how closely the line fits the data. The best R-squared value is 1.000, which means every data point touches the line. As the differences between the data points and the line grow, the r-squared value drops, with 0.000 being the lowest possible value.

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The equation and R-squared statistic of the trendline will appear on the chart. Note that the correlation of the data is very good in our example, with an R-squared value of 0.988.

The equation is in the form “Y = Mx + B,” where M is the slope and B is the y-axis intercept of the straight line.

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Now that the calibration is complete, let’s work on customizing the chart by editing the title and adding axis titles.

To change the chart title, click on it to select the text.

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Now type in a new title that describes the chart.

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To add titles to the x-axis and y-axis, first, navigate to Chart Tools > Design.

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Click the “Add a Chart Element” drop-down.

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Now, navigate to Axis Titles > Primary Horizontal.

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An axis title will appear.

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How to Do a Linear Calibration Curve in Excel (18)

To rename the axis title, first, select the text, and then type in a new title.

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Now, head to Axis Titles > Primary Vertical.

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An axis title will appear.

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Rename this title by selecting the text and typing in a new title.

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Your chart is now complete.

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Step Two: Calculate the Line Equation and R-Squared Statistic

Now let’s calculate the line equation and R-squared statistic using Excel’s built-in SLOPE, INTERCEPT, and CORREL functions.

To our sheet (in row 14) we’ve added titles for those three functions. We’ll perform the actual calculations in the cells beneath those titles.

First, we will calculate the SLOPE. Select cell A15.

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Navigate to Formulas > More Functions > Statistical > SLOPE.

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The Function Arguments window pops up. In the “Known_ys” field, select or type in the Y-Value column cells.

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In the “Known_xs” field, select or type in the X-Value column cells. The order of the ‘Known_ys’ and ‘Known_xs’ fields matters in the SLOPE function.

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Click “OK.” The final formula in the formula bar should look like this:

=SLOPE(C3:C12,B3:B12)

(Video) How to Make a Calibration Curve in Excel

Note that the value returned by the SLOPE function in cell A15 matches the value displayed on the chart.

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Next, select cell B15 and then navigate to Formulas > More Functions > Statistical > INTERCEPT.

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The Function Arguments window pops up. Select or type in the Y-Value column cells for the “Known_ys” field.

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Select or type in the X-Value column cells for the “Known_xs” field. The order of the ‘Known_ys’ and ‘Known_xs’ fields also matters in the INTERCEPT function.

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Click “OK.” The final formula in the formula bar should look like this:

=INTERCEPT(C3:C12,B3:B12)

Note that the value returned by the INTERCEPT function matches the y-intercept displayed in the chart.

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Next, select cell C15 and navigate to Formulas > More Functions > Statistical > CORREL.

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The Function Arguments window pops up. Select or type in either of the two cell ranges for the “Array1” field. Unlike SLOPE and INTERCEPT, the order does not affect the result of the CORREL function.

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Select or type in the other of the two cell ranges for the “Array2” field.

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Click “OK.” The formula should look like this in the formula bar:

=CORREL(B3:B12,C3:C12)

Note that the value returned by the CORREL function does not match the “r-squared” value on the chart. The CORREL function returns “R,” so we must square it to calculate “R-squared.”

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Click inside the Function Bar and add “^2” to the end of the formula to square the value returned by the CORREL function. The completed formula should now look like this:

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=CORREL(B3:B12,C3:C12)^2

Press Enter.

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After changing the formula, the “R-squared” value now matches the one displayed in the chart.

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Step Three: Set Up Formulas For Quickly Calculating Values

Now we can use these values in simple formulas to determine the concentration of that “unknown” solution or what input we should enter into the code so that the marble flies a certain distance.

These steps will set up the formulas required for you to be able to enter an X-value or a Y-value and get the corresponding value based on the calibration curve.

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The equation of the line-of-best-fit is in the form “Y-value = SLOPE * X-value + INTERCEPT,” so solving for the “Y-value” is done by multiplying the X-value and SLOPE and then adding the INTERCEPT.

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As an example, we put zero in as the X-value. The Y-value returned should be equal to the INTERCEPT of the line of best fit. It matches, so we know the formula is working correctly.

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Solving for the X-value based on a Y-value is done by subtracting the INTERCEPT from the Y-value and dividing the result by the SLOPE:

X-value=(Y-value-INTERCEPT)/SLOPE

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As an example, we used the INTERCEPT as a Y-value. The X-value returned should be equal to zero, but the value returned is 3.14934E-06. The value returned is not zero because we inadvertently truncated the INTERCEPT result when typing the value. The formula is working correctly, though, because the result of the formula is 0.00000314934, which is essentially zero.

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You can enter in any X-value you’d like into the first thick-bordered cell and Excel will calculate the corresponding Y-value automatically.

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Entering any Y-value into the second thick-bordered cell will give the corresponding X-value. This formula is what you would use to calculate the concentration of that solution or what input is needed to launch the marble a certain distance.

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In this case, the instrument reads “5” so the calibration would suggest a concentration of 4.94 or we want the marble to travel five units of distance so the calibration suggests we enter 4.94 as the input variable for the program controlling the marble launcher. We can be reasonably confident in these results because of the high R-squared value in this example.

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FAQs

What is the linear calibration formula? ›

Thus, the commonly used form of linear calibration function is: (2) y = a1x. where: x is independent variable (analyte content), y is function of x (analytical signal).

Can a calibration curve be a straight line? ›

One of the unsung or rather unknown important aspects in any reported BAC result is the calibration curve. It is not a curve but must be a line. It is known as analytical linearity.

How do you create a calibration curve? ›

To construct the calibration curve, use a computer program to plot the data as signal vs. concentration. Use the standard deviation of the repeated measurements for each data point to make error bars. Remove portions of the curve that are non-linear, then perform a linear regression and determine the best-fit line.

What is linear range of a calibration curve? ›

Calibration range - The calibration range is the interval between the upper and the lower concentration of the analyte which can be determined with the demonstrated precision, accuracy and response function. [ ref 7]

How do you find the linear range in Excel? ›

Select “Linear” under “Trendline Options”. Also select “Display Equation on Chart” and “Display R-Squared Value on Chart”. You should now see a dotted line drawn through your data points and a text box next to it with the best-fit linear equation and the R2 value.

Why should a calibration curve be linear? ›

Linear calibration curves are desirable because they result in the best accuracy and precision. A plot of the calibration data and the fitted line should always be examined to check for outliers and to verify linear behavior.

How do you calculate linearity? ›

linearity = |slope| (process variation) (4) The percentage linearity is calculated by: % linearity = linearity / (process variation) (5) and shows how much the bias changes as a percentage of the process variation. the coefficients. Of particular interest is the P-value for the slope.

Should calibration curve pass through origin? ›

A calibration curve (whether linear or nonlinear) must not be forced through the origin unless it is demonstrated (e.g., during method development) that the intercept (i.e., y[x = 0]) is not statistically different from zero (e.g., by performing a t-test for the y-intercept or comparing it to the MDL.)

Can a standard curve be linear? ›

The standard range is the linear portion of the standard curve in which analyte concentration can be determined accurately. Concentration should not be extrapolated from the standard curve beyond the recommended standard range; outside this range the standard curve is non-linear.

How do you draw a best fit curve in Excel? ›

Right Click on any one of the data points and a dialog box will appear. Click “Add Trendline”; this is what Excel calls a “best fit line”: 16. An options window appears and to ask what type of Trend/Regression type you want.

Is a calibration curve linear? ›

Calibration curve in bioanalytical method is a linear relationship between concentration (independent variable) and response (dependent variable) using a least squares method. This relationship is built to predict the unknown concentrations of the analyte in a complicated matrix.

What is calibration curve method? ›

Abstract: In analytical chemistry, a calibration curve is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration.

How many points is a calibration curve? ›

You need a minimum of two points on the calibration curve. The concentration of unknown samples is given by (A - intercept) / slope where A is the measured signal and slope and intercept from the first-order fit.

How do you find the linear range on a graph? ›

Identify the set of all the y-coordinates in the function's graph to determine the range. In this example, the range is {y ≥ -2}, since -2 is the lowest y-value and the arrow indicates the line continues upward. The boundary number of -2 is included, since the dot is solid.

What is linear portion of a curve? ›

The linear portion of the reaction progress curve (product versus time) is the part starting at time zero that is tangent to the curve. The slope for this linear part of the curve is the initial rate. Sometimes, if there is too much enzyme, the curve will not appear to have any linear portion.

What is R2 in calibration curve? ›

The coefficient of determination, or R2 value, is a measure of how well a set of data fits a calibration curve. This is the metric that is used almost universally by agricultural and environmental laboratories across the county.

What is a calibration curve absorbance vs concentration? ›

What's the difference between calibration curve and concentration curve? The main distinction between a calibration curve and a concentration curve is that a calibration curve is a graph of absorbance and concentration, whereas concentration is the amount of a chemical distributed in a unit volume.

How will you know if your calibration curve is acceptable? ›

The r or r2 values that accompany our calibration curve are measurements of how closely our curve matches the data we have generated. The closer the values are to 1.00, the more accurately our curve represents our detector response. Generally, r values ≥0.995 and r2 values ≥ 0.990 are considered 'good'.

What is linearity in method validation? ›

Linearity

The linearity of an analytical procedure is its ability (within a given range) to obtain test results which are directly proportional to the concentration (amount) of analyte in the sample.

Can a calibration curve be quadratic? ›

Although in principle, all systems should have a linear response to the concentration and generate linear calibration curves, in reality, some physical and chemical phenomenon can create quadratic calibration curves.

How do you find the linearity of a set of data? ›

Graphical Method:

Plot the average measured values (on the y-axis) for each sample against the reference value (on the x-axis). If the resulting line is approximates a straight line with a 45-degree slope, the measurement device is linear.

Is linearity the same as accuracy? ›

1. Measure of your measurement system's accuracy. Bias is a measure of your measurement accuracy. Linearity is how much that bias changes over the range of your process measurements.

How do you know if a data set is linear? ›

Use Simple Regression Method for Regression Problem

Linear data is data that can be represented on a line graph. This means that there is a clear relationship between the variables and that the graph will be a straight line. Non-linear data, on the other hand, cannot be represented on a line graph.

What is the slope of a calibration curve? ›

A consistent calibration curve slope is a positive indication of assay performance in a validated bioanalytical method using LC–MS/MS. It is one of the quality indica- tors utilized by bioanalytical scientists dur- ing the data review process.

Should you force the trendline through the origin? ›

Forcing the best-fit through the origin not only artifically steepens the graph's slope, but it obscures the physically meaningful y-intercept. It's perfectly acceptable, and sometimes desirable, not to begin an axis at zero.

Is adding 0 0 the same as forcing the trendline through the origin? ›

Forcing the curve through zero is not the same as including the origin as a fictitious point in the calibration.

What is linearity calibration? ›

Linearity is an objective description of the relationship between a quantitative method's final answer and true analyte concentration. Calibration brings this relationship into correspondence with calibrator concentration.

What is calibration in regression? ›

Regression calibration is a statistical method for adjusting point and interval estimates of effect obtained from regression models commonly used in epidemiology for bias due to measurement error in assessing nutrients or other variables.

What is r2 in calibration curve? ›

The coefficient of determination, or R2 value, is a measure of how well a set of data fits a calibration curve. This is the metric that is used almost universally by agricultural and environmental laboratories across the county.

What is non linear calibration? ›

Summary: Non-linear calibration is a widely used method for quantifying biomarkers wherein concentration-response curves estimated using samples of known concentrations are used to predict the biomarker concentrations in the samples of interest.

How do you calculate linearity? ›

linearity = |slope| (process variation) (4) The percentage linearity is calculated by: % linearity = linearity / (process variation) (5) and shows how much the bias changes as a percentage of the process variation. the coefficients. Of particular interest is the P-value for the slope.

Is linearity the same as accuracy? ›

1. Measure of your measurement system's accuracy. Bias is a measure of your measurement accuracy. Linearity is how much that bias changes over the range of your process measurements.

How do you calculate linearity of a balance? ›

Linearity is typically tested by placing known weights on the balance from near zero to full capacity. It is “linear” because if you graphed ideal results, you should get a fairly straight line. The plus and minus signs are a range of permissible error.

What is a calibration curve statistics? ›

In analytical chemistry, a calibration curve, also known as a standard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration.

What are the methods of calibration? ›

Different Types of Calibration
  • Pressure Calibration. ...
  • Temperature Calibration. ...
  • Flow Calibration. ...
  • Pipette Calibration. ...
  • Electrical calibration. ...
  • Mechanical calibration.
12 Feb 2021

What is calibration curve in ML? ›

Calibration curves (also known as reliability diagrams) compare how well the probabilistic predictions of a binary classifier are calibrated. It plots the true frequency of the positive label against its predicted probability, for binned predictions. The x axis represents the average predicted probability in each bin.

Is a calibration curve linear? ›

Calibration curve in bioanalytical method is a linear relationship between concentration (independent variable) and response (dependent variable) using a least squares method. This relationship is built to predict the unknown concentrations of the analyte in a complicated matrix.

What is an acceptable R2 value for a standard curve? ›

R^2 should be as close to 1 as possible. 0.9 is relatively low. This could just be due to pipetting error.

How many points is a calibration curve? ›

You need a minimum of two points on the calibration curve. The concentration of unknown samples is given by (A - intercept) / slope where A is the measured signal and slope and intercept from the first-order fit.

Can a calibration curve be non linear? ›

Using Nonlinear Calibration Curves

There are times when a linear calibration curve does not give a good fit of the calibration data. It is common in such cases to use a nonlinear function for the calibration curve. A second- or higher-order polynomial is often used in these situations.

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