Angles are measured from +x axis, in degrees. Positive y is upward. Use signs for direction if needed.
Example data table
These examples show typical inputs and outputs. Results assume the same speed unit for each row.
| Case | Mode | Inputs | Δv (x, y) | |Δv| | Δt | |ā| |
|---|---|---|---|---|---|---|
| 1 | Components | vᵢ=(3,2), v𝒻=(6,-1) | (3, -3) | 4.243 | 2 s | 2.121 m/s² |
| 2 | Scalar | vᵢ=-4, v𝒻=2 | (6, 0) | 6 | 3 s | 2 m/s² |
| 3 | Magnitude + angle | |vᵢ|=5 @ 30°, |v𝒻|=8 @ -15° | (3.456, -3.571) | 4.968 | — | — |
| 4 | Acceleration · time | a=(1,-0.5), vᵢ=(2,1), Δt=4 s | (4, -2) | 4.472 | 4 s | 1.118 m/s² |
Formula used
- Δv⃗ = v⃗𝒻 − v⃗ᵢ (vector subtraction, component-wise).
- |v⃗| = √(vₓ² + vᵧ²) and θ = atan2(vᵧ, vₓ) for direction.
- ā⃗ = Δv⃗ / Δt when a time interval is provided.
- Magnitude-angle inputs convert via vₓ = |v|cosθ, vᵧ = |v|sinθ.
- Constant-acceleration mode uses v⃗𝒻 = v⃗ᵢ + a⃗Δt.
How to use this calculator
- Select an input mode that matches your measurements.
- Choose a speed unit, then enter the required values.
- Optionally add Δt to compute average acceleration.
- Press Submit to display results above the form.
- Use the download buttons to export CSV or PDF.
Delta v as an experimental signal
Delta v is the core indicator of how motion changes during an interval. In labs, it links directly to impulse, braking performance, and turning behavior. This calculator supports signed one dimensional cases and full two dimensional vectors, so you can capture direction reversals that a simple speed change hides. Use consistent units across inputs, then review the reported magnitude and angle to confirm the physical story. It also validates simulation outputs quickly.
Component workflow for tracked motion
Component entry is best when sensors output x and y channels, such as video tracking or inertial data. By subtracting final and initial components, the tool reports delta v_x and delta v_y, then converts them into magnitude and direction using standard trigonometry. If your coordinate axes follow a map or runway, keep that convention, because the resulting direction is always referenced to the positive x axis for clearer reporting later.
Magnitude angle workflow for bearings
Magnitude and angle entry is useful for navigation style measurements, where you know a speed and a bearing. Internally, the calculator converts each vector into components with cosine and sine before subtraction. This mode is practical for projectile launch estimates, river current problems, and robotics headings. If you enter angles in degrees, use negative values for clockwise rotations to match the displayed convention. It supports wind correction by comparing two direction states.
Average acceleration as a comparison metric
When a time interval is supplied, the calculator adds average acceleration outputs. Average acceleration equals delta v divided by delta t, so it summarizes how quickly the velocity changed without assuming the acceleration was constant. For motion that is roughly uniform in its change, the reported magnitude helps compare experiments. For highly varying motion, treat the value as a useful summary, not a full model. Use repeated runs to see repeatability clearly.
Constant acceleration segments and reporting
The acceleration times time mode is designed for constant acceleration segments, where final velocity equals initial velocity plus acceleration multiplied by time. Enter acceleration in meters per second squared and time in seconds, minutes, or hours. This option is common in kinematics worksheets, drive cycle estimates, and simple control tests. After calculation, export CSV for spreadsheets or PDF for documentation and review. Include sign on acceleration components to represent thrust or drag.
FAQs
1) What does delta v represent?
Delta v is the vector difference between final and initial velocity. It captures both speed change and direction change, making it more informative than comparing speeds alone.
2) Why can speed stay constant while delta v changes?
If an object turns while keeping the same speed, the velocity direction changes. A direction change creates a nonzero delta v even when the speed magnitude remains unchanged.
3) Which input mode should I use?
Use components when you have x and y data. Use magnitude and angle for bearings. Use scalar mode for straight line motion. Use acceleration times time for constant acceleration segments.
4) How are angles interpreted in the results?
Angles are measured from the positive x axis. Counterclockwise angles are positive, and clockwise angles are negative. The direction shown is the atan2 based angle of the vector.
5) Can I enter km/h or mph?
Yes. Select your unit and enter all speeds in that unit. The calculator converts internally to meters per second and converts results back to your selected unit for display.
6) What does average acceleration mean here?
Average acceleration is delta v divided by the time interval you provide. It summarizes the overall rate of change of velocity across that interval, even if acceleration was not constant throughout.