Axis Deviation Calculator: ECG Heart Axis Explained

This axis deviation calculator works out the mean electrical axis (QRS axis) of the heart from the QRS amplitudes in leads I and aVF, which you enter in millimeters (mm) or millivolts (mV). You get the axis angle in degrees, plus a classification of normal, left, right, or extreme deviation. The calculator uses the standard arctangent formula, so you can verify the result by hand if needed.

Formula

The mean electrical axis is the net direction of ventricular depolarization in the frontal plane. It is calculated from the QRS complex amplitudes in two perpendicular limb leads, usually I (0°) and aVF (+90°). The formula is:

Axis (θ) = arctan( QRS amplitude in aVF / QRS amplitude in lead I )

Where:

• QRS amplitude in lead I = net height of the QRS complex (R wave minus S wave) in lead I, in mm (or mV).
• QRS amplitude in aVF = net height of the QRS complex in lead aVF, in mm (or mV).
• θ = the axis angle in degrees, measured from 0° (lead I) toward +90° (aVF).

Because the angle can be in any quadrant, the calculator uses the two-argument arctangent (atan2) which correctly handles negative values. If you measure amplitudes in mV, the ratio is the same, so the axis is identical.

Worked Example

Using the default values: QRS amplitude in lead I = 8 mm, QRS amplitude in aVF = 4 mm.

1. Compute the ratio: 4 / 8 = 0.5.
2. Find the arctangent: arctan(0.5) ≈ 26.565°.
3. Because both amplitudes are positive, the axis is in the normal quadrant (0° to +90°).
4. The calculator rounds to one decimal place: 26.6°.

This is a normal axis (between -30° and +90°). The category output returns 1 for normal.

How to Measure QRS Amplitudes

To get the numbers for the calculator, look at a standard 12-lead ECG. For each lead (I and aVF), find the QRS complex—the first upward or downward deflection after the P wave. Measure the net amplitude:

• If the QRS is mostly upright, measure from the top of the R wave to the baseline (or subtract the S wave depth if present).
• If the QRS is mostly negative, measure the depth of the S wave below the baseline and treat it as a negative number.
• Use the same unit (mm or mV) for both leads—the ratio is what matters.

Standard ECG paper runs at 25 mm/s, and 1 mV = 10 mm. So 1 mm = 0.1 mV. Many modern ECG machines display amplitudes in mm, but you can convert easily.

Interpreting the Result

The axis angle tells you the average direction of electrical flow during ventricular depolarization. Normal axis is between -30° and +90°. Outside that range:

• Left axis deviation (LAD): -30° to -90°. Often seen with left anterior fascicular block, inferior myocardial infarction, or left ventricular hypertrophy.
• Right axis deviation (RAD): +90° to +180°. Common in right ventricular hypertrophy, chronic lung disease, or left posterior fascicular block.
• Extreme axis deviation (northwest axis): -90° to -180° (or 180° to 270°). This is rare and may indicate severe right ventricular strain or hyperkalemia.

Remember that the axis alone is not a diagnosis—it is a clue that must be interpreted with the full ECG and clinical picture.

Common Mistakes and Limitations

The most frequent error is using the wrong leads or measuring the QRS incorrectly. The formula assumes you are using leads I and aVF, which are perpendicular. If you use other leads, the angle will be different. Another mistake is forgetting to include the S wave when the QRS is biphasic—always take the net amplitude (R – S).

The formula also assumes a single mean vector, which oversimplifies the heart’s electrical activity. In reality, the QRS axis can vary with body habitus, pregnancy, age, and even electrode placement. The calculator gives a numerical estimate, not a definitive measurement. For clinical decisions, always confirm with a physician or a formal ECG interpretation.

Alternatives to the Formula

If you don’t want to compute the axis manually, you can use the quadrant method: look at the net QRS deflection in leads I and aVF. If both are positive, the axis is normal. If lead I is positive and aVF is negative, it’s left deviation. If lead I is negative and aVF is positive, it’s right deviation. If both are negative, it’s extreme deviation. This quick check is useful for bedside interpretation but doesn’t give a precise angle.

Some ECG machines automatically print the axis, but they may use different algorithms (e.g., based on multiple leads). The manual method is still taught because it helps you understand the vector concept.

Frequently Asked Questions

What is a normal QRS axis?

A normal QRS axis is between -30° and +90°. This range covers the majority of healthy adults. Some sources use -30° to +100°, but the -30° to +90° range is the most commonly taught in clinical guidelines.

Can I use this calculator for children?

Children have a different normal axis range—newborns often have right axis deviation (up to +180°), which gradually shifts leftward with age. This calculator uses adult criteria, so it may misclassify a pediatric ECG. Use pediatric-specific reference ranges for interpretation.

What if my QRS amplitude is negative in both leads?

If both leads have negative net amplitudes, the axis will be in the extreme deviation range (between -90° and -180°). This is rare and often indicates a serious condition, so it should be evaluated by a healthcare professional immediately.

Do I need to convert mm to mV?

No, because the formula uses a ratio. As long as you use the same unit for both leads, the axis angle is the same. However, if you want to double-check with a different method, consistency is key.

Why does my ECG machine show a different axis?

ECG machines often use more than two leads to calculate the axis, and they may apply filtering or averaging. The manual two-lead method is a simplified approximation. Small differences are expected and usually not clinically significant.

Related

• Correlation Coefficient: Formula and Calculation
• Specificity From a Confusion Matrix: Formula and Example
• Calculate Relative Error: Formula and Examples

in qrs_i | QRS amplitude in lead I | mm | 8 | 0
in qrs_avf | QRS amplitude in lead aVF | mm | 4 | 0
out axis | QRS axis | degrees | atan2(qrs_avf, qrs_i) * 180 / pi | 1
out category | Category | - | if(axis > -30 and axis  90 and axis  -90 and axis