Calculate how long a vertical drop or throw takes, plus the landing speed and maximum height, with clear up/down sign rules and unit options.
Advanced options
How to use our Free Fall Calculator
- Pick Solve for to match what you want to find (for example, time from a starting height).
- Choose a Unit system so your heights and speeds are in the right units (feet for US, meters for Metric).
- Enter Gravitational acceleration g (selected unit) as a positive number (use the default Earth value unless your problem gives a different g).
- Enter Starting height above landing point y0 (selected unit). If you start at the landing point, enter 0.
- Enter Initial vertical velocity v0 (selected unit). Use 0 for a drop from rest. If it is thrown, the sign depends on your Positive direction choice in Advanced options.
- Open Advanced options and set Positive direction (Up is positive or Down is positive). This controls the sign of the signed velocity results.
- If the landing point is not at 0, set Landing height y_land (selected unit) (often 0 for ground).
- Optional: Turn on Air resistance model and enter Terminal speed (selected unit) if you want a simple real-world-style estimate (it will usually predict a slower fall and a lower impact speed than ideal).
- Optional: Set Number display (Auto is best for most cases; Scientific helps for extremely large or tiny values).
- Click Calculate, then sanity-check: if Air resistance model is None and you double the height (with the same g and v0 = 0), the time should increase by about a factor of 1.41 (square root of 2), and the impact speed should increase by about a factor of 1.41.
Definitions
Free fall: Vertical motion where gravity is the main force. In the ideal model, air resistance is ignored. [3]
Gravitational acceleration g: How strongly gravity accelerates an object. You enter g as a positive number; the calculator applies the sign based on your Positive direction setting.
Positive direction: Your choice of which way is positive (Up is positive or Down is positive). This affects the sign of Initial vertical velocity v0 (selected unit) and Velocity at landing (signed).
Velocity (signed): Speed with direction, so it can be positive or negative. [2]
Speed (magnitude): How fast something moves without direction. It is always 0 or higher.
Terminal speed: The steady maximum falling speed in air when drag balances weight. [1]
Common mistakes and quick fixes
Mistake: Entering Gravitational acceleration g (selected unit) as 0, negative, or leaving it blank.
Fix: g must be a positive number. Use the default value for your chosen Unit system if you are not sure.
Mistake: Switching Positive direction but not updating the sign of Initial vertical velocity v0 (selected unit) .
Fix: Decide what counts as positive first. If Up is positive, upward throws have v0 > 0 and downward throws have v0
Mistake: Setting the landing point above the start (y_land greater than y0) and expecting a landing time when the object is moving away from that point.
Fix: Check that the motion can actually reach Landing height y_land (selected unit) . If it cannot, Time to reach landing height should show N/A and the Notes or warnings output should explain what to change.
Mistake: Turning on Air resistance model but using a non-positive Terminal speed (selected unit) (0, negative, or blank).
Fix: Enter a terminal speed greater than 0, or set Air resistance model back to None (ideal free fall).
Mistake: Treating Velocity at landing (signed) like a speed and thinking a negative value means the math is wrong.
Fix: Use Speed at landing (magnitude) to answer "how fast" (always non-negative). Use the signed velocity only to show direction based on Positive direction .
Mistake: Expecting a larger Maximum height reached (if thrown upward) even when v0 is not upward in your chosen sign convention.
Fix: The object only has a higher peak if it starts with an upward velocity in your sign setup. Otherwise, max height equals the start height and Time to reach maximum height (if any) is 0.
Methodology
Sign setup (used in all modes): You enter g as a positive magnitude. The calculator sets acceleration a based on your Positive direction choice.
a = -g (Up is positive) or a = +g (Down is positive)
Ideal free fall (no air resistance): This uses the constant-acceleration kinematics equations for 1D motion. [3]
y(t) = y0 + v0*t + 0.5*a*t^2
v(t) = v0 + a*t
To find Time to reach landing height, solve for t when y(t) equals y_land. This is a quadratic equation. The calculator chooses the smallest real solution with t >= 0. If there is no real solution (or all real solutions are negative), time is N/A.
y_land = y0 + v0*t + 0.5*a*t^2
Then it computes landing velocity and speed:
impact_velocity_signed = v(t_land)
impact_speed = |impact_velocity_signed|
Maximum height (peak): If the motion reaches a point where the signed velocity becomes 0 before landing, that point is the peak. If it never goes upward in your sign setup, the calculator reports time_to_peak = 0 and max_height = y0.
t_peak = -v0/a (only if this is positive)
y_peak = y0 - v0^2/(2*a)
Optional air resistance (terminal-speed linear drag): Terminal speed is a real idea. [1] For simpler math, the calculator converts inputs into an internal down-positive system (so g > 0 and terminal speed vT > 0), uses the equations below, then converts the signed outputs back to your chosen sign convention.
v(t) = vT + (v0 - vT)*exp(-(g/vT)*t)
y(t) = y0 + vT*t + (v0 - vT)*(vT/g)*(1 - exp(-(g/vT)*t))
Time to reach y_land in the air-resistance mode is found numerically (bisection): the calculator searches for a time interval where y(t) crosses y_land, then repeatedly halves that interval until the height error is small or it hits a safe iteration limit. If the height never crosses y_land, time is N/A.
Mini-example (ideal mode): Metric units, Up is positive, g = 9.80665 m/s^2, y0 = 10 m, y_land = 0 m, v0 = 0 m/s. Then a = -9.80665. Solve 0 = 10 + 0.5*(-9.80665)*t^2, so t_land = sqrt(2*10/9.80665) = 1.428 s (about). Impact velocity is v = 0 + (-9.80665)*1.428 = -14.01 m/s, so impact speed is 14.01 m/s.
Limitations & Key Assumptions / Boundary Conditions
Ideal mode assumes constant g and no air resistance. Real falls can differ due to air drag, wind, and changes in body position, and g changes slightly with altitude.
The air-resistance option uses a simple terminal-speed (linear drag) model. Many real situations are closer to drag proportional to speed squared, so treat this mode as a rough estimate, not a lab-grade prediction.
This is 1D vertical motion only. It does not model sideways motion, launch angles, rotation, lift, bouncing, or impacts before reaching Landing height y_land (selected unit).
If the object never reaches the landing height under your inputs (for example, it is thrown upward away from the landing point), the calculator will show N/A for time-to-land instead of forcing an impossible answer.
Changing Positive direction changes the signs you see, but it does not change the real-world motion. A negative signed velocity is not automatically "bad".
Extreme values (very large heights, extremely large speeds, or very small/large g) can make the air-resistance numerical solve fail to bracket a landing time. In that case, try more realistic inputs or use ideal mode.