Calibration Curve Calculator

To create a Calibration Curve, input your Standard Concentrations and corresponding Signal Measurements in calculator, enter each pair of values in provided fields.

The calculator will generate a Linear Regression analysis, providing the Slope, Y-intercept, R² Value, and Linear Equation. Use this equation to determine Unknown Concentrations from their measured signals.

How to Calculate Calibration Curve?

To calculate a Calibration Curve, prepare a series of Standard Solutions with known concentrations and measure their signals. Plot Signal Response (y-axis) against Concentration (x-axis). Apply Linear Regression to find the best-fit line through these points.

The resulting equation (y = mx + b) allows you to calculate unknown concentrations from measured signals. Verify Linear Relationship using the R² Value, which should be close to 1.0 for reliable calibrations.

Formula for Calibration Curve Calculations

Linear Regression Equation:

y = mx + b
where:
y = Signal Response
x = Concentration
m = Slope
b = Y-intercept

Slope Calculation:

m = [n∑(xy) - (∑x)(∑y)] / [n∑(x²) - (∑x)²]
where:
n = Number of data points
x = Concentration values
y = Signal values

Y-intercept Calculation:

b = [∑y - m(∑x)] / n
where:
∑y = Sum of signal values
∑x = Sum of concentration values
n = Number of data points

R² (Correlation Coefficient) Calculation:

R² = {[n∑(xy) - (∑x)(∑y)]²} / {[n∑(x²) - (∑x)²][n∑(y²) - (∑y)²]}
where:
n = Number of data points
x, y = Paired data values

Example 1: UV-Vis Spectroscopy

• Standard Solutions: 5 concentrations
• Concentrations (mg/L): 0, 2, 4, 6, 8
• Absorbance Values: 0.000, 0.201, 0.399, 0.598, 0.800
• Slope: 0.1000
• Y-intercept: 0.0000
• R²: 0.9999

Example 2: Fluorescence Analysis

• Standard Solutions: 6 concentrations
• Concentrations (µM): 0, 5, 10, 15, 20, 25
• Fluorescence Intensity: 10, 235, 460, 685, 910, 1135
• Slope: 45.0
• Y-intercept: 10.0
• R²: 0.9998

Example 3: HPLC Calibration

• Standard Solutions: 4 concentrations
• Concentrations (ppm): 1, 5, 10, 20
• Peak Area: 1050, 5200, 10400, 20800
• Slope: 1040
• Y-intercept: 10
• R²: 0.9999

Example 4: Ion Selective Electrode

• Standard Solutions: 5 concentrations
• Concentrations (mM): 0.1, 1.0, 10, 100, 1000
• Voltage (mV): -58.0, -29.0, 0.0, 29.0, 58.0
• Slope: 29.0
• Y-intercept: 0.0
• R²: 0.9997

Example 5: Calculate y for Known x

Given x = 3.5, find y. y = mx + b = 0.2 3.5 + 0 = 0.7 y = mx + b = 0.2 3.5 + 0 = 0.7

What is Calibration Curve?

The Calibration Curve is typically established using Linear Regression Analysis, though non-linear relationships may occur in some cases. The quality of the calibration is assessed through the R² Value, which indicates how well the data fits the model. Calibration Curves are essential for various analytical techniques including Spectroscopy, Chromatography, and Electrochemical Analysis.