IP331.com | Online Tools
HomeTrigonometry ToolsVertical Shift Calculator

Vertical Shift Calculator

Find vertical shift and midline of a sine or cosine graph

Vertical Shift Formula

midline: y = D

Vertical shift moves a sine or cosine graph up or down. In standard form, the constant D gives both the vertical shift and the graph midline.

This calculator reads D from y=A sin(Bx+C)+D or y=A cos(Bx+C)+D. Positive D shifts upward, negative D shifts downward.

How Vertical Shift Works

The sinusoidal wave oscillates around its midline. Adding D changes that center line without changing amplitude or period.

Constant D

The added constant controls shift.

Midline

The midline is y=D.

Up or Down

Positive shifts up, negative shifts down.

Separate From Amplitude

Amplitude controls wave height.

💡 Example: For y=3cos(x)-2, D=-2 and the midline is y=-2.

Applications of Vertical Shift

Trig GraphsSinusoidal ModelsTidesWave Data

Frequently Asked Questions

What is a vertical shift calculator?
It identifies the vertical shift and midline of a sine or cosine function.
What is the vertical shift formula?
For y=A sin(Bx+C)+D or y=A cos(Bx+C)+D, the vertical shift is D and the midline is y=D.
How do I use this calculator?
Enter the constant D and click Calculate.
Is vertical shift the same as amplitude?
No. Amplitude controls height from the midline, while vertical shift moves the midline up or down.
Where is vertical shift used?
It is used in trig graphing, sinusoidal modeling, waves, tides, and data fitting.

More Trigonometry Tools

Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.

© 2026 IP331.com — Free Online Tools. All rights reserved.

About · Contact · Privacy Policy · Cookie Policy · Terms of Use · Disclaimer · Sitemap