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Kinematic Equations Calculator — Solve SUVAT Instantly

Q: What is the standard value of gravitational acceleration g?

Per NIST, standard gravity is exactly **9.80665 m/s²**, rounded to **9.81 m/s²** for most physics problems. In practice it varies from 9.780 m/s² at the equator to 9.832 m/s² at the poles due to Earth's shape and rotation. For engineering and graded physics, always use 9.81 m/s² unless the problem specifies otherwise.

Q: Why does stopping distance quadruple when speed doubles?

Because stopping distance depends on the **square** of initial velocity: from v² = v₀² + 2ad with v = 0, we get d = v₀²/(2|a|). Doubling v₀ quadruples d. At 60 km/h with a = −8 m/s²: d ≈ 17.4 m. At 120 km/h: d ≈ 69.4 m — exactly four times longer. This exponential relationship is why speed limits have disproportionately large safety effects.

Q: Are kinematic equations valid in space or zero-gravity environments?

Yes. SUVAT equations are valid wherever acceleration is **constant**, regardless of gravity. In microgravity aboard the ISS, an astronaut pushed by a constant force follows d = v₀t + ½at² perfectly. The only difference is that 'g' is effectively zero for unsupported objects, so free-fall acceleration doesn't apply. Rocket thrust producing constant thrust-to-mass ratio is a textbook constant-acceleration SUVAT scenario.

Enter initial velocity, acceleration, and time to instantly get final velocity and displacement. Covers all four SUVAT equations with worked examples, reference table, and free-fall, braking, and projectile scenarios.

Data verified · June 2026
Edited by Martín Rodríguez
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Edited by: Martín Rodríguez (editorial policy ) · Last editorial review: Jun 22, 2026

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The Kinematic Equations Calculator solves motion problems under constant acceleration using the four core SUVAT equations of classical mechanics. Enter initial velocity (v₀), acceleration (a), and time (t) to get final velocity and displacement instantly — or use the equations below to solve for any missing variable. Applies to free-fall (g = 9.81 m/s²), emergency braking, projectile launch, and any uniformly accelerated linear motion. Units: SI (m, s, m/s, m/s²).

When to use this calculator

Calculating how far a car travels before stopping given initial speed and braking deceleration (v₀ = 27.8 m/s ≈ 100 km/h, a = −8 m/s² → stopping distance ≈ 48.2 m)
Determining final velocity and drop distance in free fall (a = 9.81 m/s², t = 3 s → v = 29.43 m/s, d = 44.1 m)
Finding acceleration of a rocket sled that goes from rest to 300 m/s over 400 m of track (a = v²/2d = 112.5 m/s²)
Solving for flight time of a ball thrown upward at v₀ = 20 m/s (total time = 4.08 s, max height = 20.4 m)

Surface gravity by celestial body (use as 'a' for free-fall problems)

Body	Surface gravity g (m/s²)	Relative to Earth
Sun	274.0	27.9×
Jupiter	24.79	2.53×
Neptune	11.15	1.14×
Saturn	10.44	1.06×
Earth	9.807	1.00×
Venus	8.87	0.90×
Uranus	8.69	0.89×
Mars	3.71	0.38×
Mercury	3.70	0.38×
Moon	1.62	0.17×
Pluto	0.7	0.07×

Plug these values in as the acceleration a in the SUVAT equations to solve free-fall problems on other worlds. Earth's value is standard gravity, exactly 9.80665 m/s² (NIST). A 3-second drop from rest reaches v = g × 3 — e.g. 29.4 m/s on Earth but only 4.9 m/s on the Moon.

How it works

The Four Kinematic (SUVAT) Equations

All four equations assume constant acceleration throughout the interval. The five SUVAT variables:

Symbol	Variable	SI Unit
v₀	Initial velocity	m/s
v	Final velocity	m/s
a	Acceleration	m/s²
t	Time elapsed	s
d	Displacement	m

The four fundamental equations:

(1)  v  = v₀ + a·t           [missing d]
(2)  d  = v₀·t + ½·a·t²      [missing v]
(3)  v² = v₀² + 2·a·d        [missing t]
(4)  d  = ½·(v₀ + v)·t       [missing a]

This calculator uses Equations 1 and 2 (given v₀, a, t → finds v and d).

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Reference Table — Common Constant-Acceleration Scenarios

Scenario	v₀ (m/s)	a (m/s²)	t (s)	v (m/s)	d (m)
Free fall from rest, 1 s	0	9.81	1	9.81	4.91
Free fall from rest, 3 s	0	9.81	3	29.43	44.15
Free fall from rest, 5 s	0	9.81	5	49.05	122.6
Free fall from rest, 10 s	0	9.81	10	98.1	490.5
Car braking: 60 km/h → 0	16.67	−8.0	2.08	0	17.4
Car braking: 100 km/h → 0	27.78	−8.0	3.47	0	48.2
Car braking: 120 km/h → 0	33.33	−8.0	4.17	0	69.4
Sprinter: 0 → 10 m/s in 4 s	0	2.5	4	10	20
Ball thrown up at 20 m/s (to peak)	20	−9.81	2.04	0	20.4
Rocket sled: 0 → 300 m/s, 400 m	0	112.5	2.67	300	400

g = 9.81 m/s² (standard gravity per NIST). Braking assumes dry asphalt, ABS engaged.

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Which Equation To Use — Quick Guide

You know	You want	Use equation
v₀, a, t	v and d	(1) and (2) ← this calculator
v₀, a, d	v and t	(3) then (1)
v₀, v, t	a and d	(1) rearranged, then (4)
v₀, v, a	t and d	(1) rearranged, then (3)
v₀, v, d	a and t	(3) rearranged, then (4)

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Worked Examples

Free Fall — Stone Dropped from a Cliff

v₀ = 0, a = +9.81 m/s², t = 3 s:

v = 0 + 9.81 × 3 = 29.43 m/s
d = 0 + ½ × 9.81 × 9 = 44.15 m   (~14-story building)

Emergency Braking — 100 km/h

v₀ = 27.78 m/s, a = −8 m/s², v = 0:

0 = 27.78² + 2×(−8)×d  →  d = 771.7/16 = 48.2 m
t = (0 − 27.78)/(−8) = 3.47 s

Stopping distance nearly doubles every time you add 30 km/h because d ∝ v₀².

Upward Projectile — Ball Thrown at 20 m/s

v₀ = 20 m/s, a = −9.81 m/s²:

Peak: t = 20/9.81 = 2.04 s,  d_max = 20×2.04 − ½×9.81×2.04² = 20.4 m
Total flight (back to ground) = 4.08 s  (symmetry)

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Common Mistakes

1. Sign of acceleration — deceleration must be entered as a negative value (e.g., −8 m/s² for braking). Entering +8 m/s² models a speeding-up scenario and gives wildly wrong results.
2. g = 10 vs 9.81 — 10 m/s² is acceptable for rough estimates but introduces a 1.9% error. Use 9.81 m/s² (NIST) in graded problems.
3. Displacement ≠ distance — SUVAT gives displacement (vector). If the object reverses direction mid-interval (e.g., ball thrown up then falling), total distance ≠ displacement.
4. Non-constant acceleration — SUVAT is invalid for variable forces (air drag, springs). Use calculus (∫a dt) or numerical integration instead.
5. Mixed units — convert everything to SI (m, s, m/s, m/s²) before plugging in. 1 km/h = 0.2778 m/s.

Worked Example: Object in Free Fall

A stone is dropped from rest: v₀ = 0 m/s, a = 9.81 m/s², t = 3 s

Final velocity: v = 0 + 9.81 × 3 = 29.43 m/s [Eq. 1: v = v₀ + at]

Distance fallen: d = 0×3 + ½×9.81×3² = 44.15 m [Eq. 2: d = v₀t + ½at²]

After 3 seconds: v = 29.43 m/s, d = 44.15 m (≈ 14-story building)

Frequently asked questions

What are the four kinematic (SUVAT) equations?

The four kinematic equations for constant acceleration are: (1) v = v₀ + at — links v, v₀, a, t; (2) d = v₀t + ½at² — links d, v₀, a, t; (3) v² = v₀² + 2ad — links v, v₀, a, d (no time); (4) d = ½(v₀ + v)t — links d, v₀, v, t (no acceleration). Each omits one of the five SUVAT variables, so you choose the equation that matches the three variables you know.

What is the standard value of gravitational acceleration g?

Per NIST, standard gravity is exactly 9.80665 m/s², rounded to 9.81 m/s² for most physics problems. In practice it varies from 9.780 m/s² at the equator to 9.832 m/s² at the poles due to Earth's shape and rotation. For engineering and graded physics, always use 9.81 m/s² unless the problem specifies otherwise.

How do I convert km/h to m/s for these equations?

Divide by 3.6: 1 km/h = 1/3.6 m/s ≈ 0.2778 m/s. Common conversions: 60 km/h = 16.67 m/s, 80 km/h = 22.22 m/s, 100 km/h = 27.78 m/s, 120 km/h = 33.33 m/s. Always convert to m/s before plugging into SUVAT to keep units consistent.

Why does stopping distance quadruple when speed doubles?

Because stopping distance depends on the square of initial velocity: from v² = v₀² + 2ad with v = 0, we get d = v₀²/(2|a|). Doubling v₀ quadruples d. At 60 km/h with a = −8 m/s²: d ≈ 17.4 m. At 120 km/h: d ≈ 69.4 m — exactly four times longer. This exponential relationship is why speed limits have disproportionately large safety effects.

Can SUVAT be used for 2D projectile motion?

Yes — decompose into two independent 1D problems. Horizontally: a_x = 0, so d_x = v₀·cos(θ)·t (constant velocity). Vertically: a_y = −9.81 m/s², apply Equations 1 and 2. Solve each axis separately with SUVAT, then combine for range, max height, and flight time. Air resistance is ignored in this standard model.

What if acceleration is zero — do the equations still work?

Yes. When a = 0 the equations simplify to uniform motion: v = v₀ (constant) and d = v₀·t. This is Newton's first law in equation form — no net force, no acceleration, constant speed. SUVAT handles zero acceleration as a special case automatically.

What is the difference between deceleration and negative acceleration?

Deceleration means the speed (magnitude of velocity) is decreasing. In SUVAT, this is modelled as negative acceleration when motion is in the positive direction. For braking from 100 km/h (positive forward), enter a = −8 m/s². If you define positive as downward (free fall), then g = +9.81 m/s² and upward throws require a = −9.81 m/s². The sign depends on the reference direction you choose.

Are kinematic equations valid in space or zero-gravity environments?

Yes. SUVAT equations are valid wherever acceleration is constant, regardless of gravity. In microgravity aboard the ISS, an astronaut pushed by a constant force follows d = v₀t + ½at² perfectly. The only difference is that 'g' is effectively zero for unsupported objects, so free-fall acceleration doesn't apply. Rocket thrust producing constant thrust-to-mass ratio is a textbook constant-acceleration SUVAT scenario.

How accurate are these kinematic equations for real-world problems?

They are exact for idealized constant-acceleration motion. In practice, accuracy depends on how constant the acceleration actually is: free fall in a vacuum is highly accurate; a car braking on dry asphalt (ABS) is a reasonable approximation; a ball in air deviates because drag increases with velocity squared. For speeds above ~30 m/s, air resistance typically causes 5–15% error in distance calculations compared to SUVAT predictions.

Sources & references

Methodology & trust

Editorial

Calculadora de ciencia revisada por el equipo editorial de Hacé Cuentas, contrastada con NIST – Standard Acceleration of Gravity (g = 9.80665 m/s²), según nuestra política editorial y metodología.

Updates

Última revisión: June 22, 2026. Los parámetros se verifican periódicamente con las fuentes citadas.

Privacy

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Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

Rodríguez, M. (2026). Kinematic Equations Calculator — Solve SUVAT Instantly. Hacé Cuentas. https://hacecuentas.com/kinematic-equations-constant-acceleration

Contenido bajo licencia CC-BY 4.0 — reutilizable citando la fuente con enlace a Hacé Cuentas.

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