Calculator Form
Use signed values. A negative acceleration commonly represents gravity when upward is treated as positive.
Example Data Table
| Case | Given Values | Formula Path | Result |
|---|---|---|---|
| Final velocity from height | u = 0 m/s, a = 9.81 m/s², h = 20 m | v² = u² + 2ah | v ≈ 19.81 m/s |
| Height from time | u = 12 m/s, t = 3 s, a = -9.81 m/s² | h = ut + ½at² | h ≈ -8.145 m |
| Height from velocities | u = 25 m/s, v = 5 m/s, a = -9.81 m/s² | h = (v² - u²) / 2a | h ≈ 30.58 m |
| Final velocity from time | u = 18 m/s, t = 2.5 s, a = -9.81 m/s² | v = u + at | v ≈ -6.525 m/s |
Formula Used
v = u + at
h = ut + ½at²
v² = u² + 2ah
h = (v² − u²) / 2a
These equations come from constant-acceleration kinematics. Use one sign convention throughout the problem. If upward is positive, gravity is usually entered as a negative value on Earth.
How to Use This Calculator
- Select the calculation mode that matches your known values.
- Choose a gravity preset or enter a custom acceleration.
- Fill in the needed motion inputs using consistent signs.
- Choose decimal places and graph detail if desired.
- Press Calculate to show the result above the form.
- Review the table, notes, graph, and example section.
- Download the result as CSV or PDF when needed.
FAQs
1) What does this calculator solve?
It solves height or final velocity for motion with constant acceleration. You can work from velocity, time, acceleration, and height in several combinations.
2) When should I use negative acceleration?
Use negative acceleration when your positive direction is upward and gravity acts downward. The same sign convention must stay consistent across every entered value.
3) Can this calculator handle free-fall problems?
Yes. Choose the Earth gravity preset and enter values that match your sign convention. The formulas work well for free-fall and vertical launch examples.
4) Why do I get a negative height?
A negative height usually means the object moved below the selected origin or the chosen sign convention makes downward displacement negative. Check your reference point.
5) Why does the calculator show no real velocity?
That happens when the expression inside the square root becomes negative. The entered height, acceleration, and starting velocity do not produce a real solution together.
6) What units should I enter?
Use meters for height, seconds for time, meters per second for velocity, and meters per second squared for acceleration. Keep every field in matching SI units.
7) What does the graph represent?
The graph plots height and velocity against time using your calculated motion values. It helps you inspect how position and speed change during the interval.
8) Can I save the result for reports?
Yes. Use the CSV button for spreadsheet-style records and the PDF button for a neat downloadable summary of the current result table.