Relative Velocity With Angle Calculator

Enter Motion Inputs

Use the form below to compare two moving objects. The overall page stays single-column, while the input area shifts to 3, 2, and 1 columns responsively.

Object A label

Object A speed

Object A angle (°)

Object B label

Object B speed

Object B angle (°)

Result perspective

Angle reference

Speed unit

Time interval

Time unit

Decimal places

Math angles are measured counterclockwise from east. Bearing angles are measured clockwise from north.

Example Data Table

These examples assume the math-angle convention, measured counterclockwise from east.

Case	Object A	Object B	Perspective	Relative Vector	Magnitude	Direction	5–10 s Displacement
Perpendicular motion	10 m/s @ 0°	10 m/s @ 90°	B relative to A	(-10, 10) m/s	14.14 m/s	135°	70.71 m in 5 s
Same heading	25 m/s @ 45°	40 m/s @ 45°	B relative to A	(10.61, 10.61) m/s	15.00 m/s	45°	150.00 m in 10 s
Opposite directions	30 m/s @ 0°	20 m/s @ 180°	B relative to A	(-50, 0) m/s	50.00 m/s	180°	150.00 m in 3 s
Matched motion	12 m/s @ 270°	12 m/s @ 270°	B relative to A	(0, 0) m/s	0.00 m/s	Not defined	0.00 m in 8 s

Formula Used

The calculator resolves both velocity vectors into components, subtracts them according to the selected perspective, then rebuilds the result.

1) Resolve each velocity into x and y components
v_x = v cos(θ)
v_y = v sin(θ)

2) Build the relative vector
v_rel = v_B - v_A or v_rel = v_A - v_B

3) Find the relative speed magnitude
|v_rel| = √(v_rel,x² + v_rel,y²)

4) Find the direction angle
θ_rel = atan2(v_rel,y, v_rel,x)

5) Cross-check with the law of cosines
|v_rel| = √(v_A² + v_B² - 2v_Av_Bcos(α))
where α is the included angle between the two paths.

6) Relative displacement over a time interval
d = |v_rel| × t

For bearing input, the calculator converts the bearing to a standard math angle internally using θ_math = 90° - θ_bearing.

How to Use This Calculator

Enter labels for both objects so the result reads clearly.
Choose the speed unit and angle reference that match your problem.
Enter each object’s speed and direction angle.
Select whether you want B relative to A or A relative to B.
Add a time interval if you also want relative displacement.
Pick the number of decimal places and click the calculate button.
Review the magnitude, direction, components, graph, and export options.

Frequently Asked Questions

1) What does relative velocity mean?

Relative velocity describes how fast one object appears to move from another object’s point of view. It combines speed difference and direction difference into one vector result.

2) Why does the order of subtraction matter?

Because A relative to B is the opposite vector of B relative to A. They have the same magnitude, but their directions differ by 180°.

3) Should I use math angles or bearings?

Use math angles for standard x-y physics problems. Use bearings for navigation, map work, marine problems, and any question where direction is stated clockwise from north.

4) Can relative velocity be zero?

Yes. That happens when both objects have identical speed and direction. In that case, one object appears stationary relative to the other.

5) Why is there a cosine-law check?

It verifies the magnitude using the included angle between the two velocity vectors. Matching values confirm the component method was applied correctly.

6) What does relative displacement after time mean?

It is the distance covered by the relative velocity vector during the chosen interval. It helps estimate separation change when both motions remain constant.

7) Which units does this page support?

It supports m/s, km/h, mph, ft/s, and knots for speed, plus seconds, minutes, and hours for time. The displacement output follows the chosen speed unit family.

8) Can I use this for boats, aircraft, or moving platforms?

Yes. It works well for navigation, pursuit, crossing paths, wind-relative motion, current-relative motion, and observer-frame comparisons in mechanics.